proteus: subsurfaceTransportFunctions.c Source File

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#else

  #define __Pyx_SET_REFCNT(obj, refcnt) Py_REFCNT(obj) = (refcnt)

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  #define __Pyx_PySequence_SIZE(seq)  PySequence_Size(seq)

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#if PY_MAJOR_VERSION >= 3

  #define PyIntObject                  PyLongObject

  #define PyInt_Type                   PyLong_Type

  #define PyInt_Check(op)              PyLong_Check(op)

  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)

  #define PyInt_FromString             PyLong_FromString

  #define PyInt_FromUnicode            PyLong_FromUnicode

  #define PyInt_FromLong               PyLong_FromLong

  #define PyInt_FromSize_t             PyLong_FromSize_t

  #define PyInt_FromSsize_t            PyLong_FromSsize_t

  #define PyInt_AsLong                 PyLong_AsLong

  #define PyInt_AS_LONG                PyLong_AS_LONG

  #define PyInt_AsSsize_t              PyLong_AsSsize_t

  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask

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#if PY_MAJOR_VERSION >= 3

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#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY

  #ifndef PyUnicode_InternFromString

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#if PY_VERSION_HEX < 0x030200A4

  typedef long Py_hash_t;

  #define __Pyx_PyInt_FromHash_t PyInt_FromLong

  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong

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  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t

  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t

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#if PY_MAJOR_VERSION >= 3

  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? ((void)(klass), PyMethod_New(func, self)) : __Pyx_NewRef(func))

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  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)

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#if CYTHON_USE_ASYNC_SLOTS

  #if PY_VERSION_HEX >= 0x030500B1

    #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods

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    #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))

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  #define __Pyx_PyType_AsAsync(obj) NULL

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#ifndef __Pyx_PyAsyncMethodsStruct

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#endif


#if defined(WIN32) || defined(MS_WINDOWS)

  #define _USE_MATH_DEFINES

#endif

#include <math.h>

#ifdef NAN

#define __PYX_NAN() ((float) NAN)

#else

static CYTHON_INLINE float __PYX_NAN() {

  float value;

  memset(&value, 0xFF, sizeof(value));

  return value;

}

#endif

#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)

#define __Pyx_truncl trunc

#else

#define __Pyx_truncl truncl

#endif


#define __PYX_MARK_ERR_POS(f_index, lineno) \

    { __pyx_filename = __pyx_f[f_index]; (void)__pyx_filename; __pyx_lineno = lineno; (void)__pyx_lineno; __pyx_clineno = __LINE__; (void)__pyx_clineno; }

#define __PYX_ERR(f_index, lineno, Ln_error) \

    { __PYX_MARK_ERR_POS(f_index, lineno) goto Ln_error; }


#ifndef __PYX_EXTERN_C

  #ifdef __cplusplus

    #define __PYX_EXTERN_C extern "C"

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    #define __PYX_EXTERN_C extern

  #endif

#endif


#define __PYX_HAVE__subsurfaceTransportFunctions

#define __PYX_HAVE_API__subsurfaceTransportFunctions

/* Early includes */

#include <string.h>

#include <stdio.h>

#include "numpy/arrayobject.h"

#include "numpy/ufuncobject.h"


    /* NumPy API declarations from "numpy/__init__.pxd" */


#include "math.h"

#ifdef _OPENMP

#include <omp.h>

#endif /* _OPENMP */


#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)

#define CYTHON_WITHOUT_ASSERTIONS

#endif


typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;

                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;


#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0

#define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0

#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8)

#define __PYX_DEFAULT_STRING_ENCODING ""

#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString

#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize

#define __Pyx_uchar_cast(c) ((unsigned char)c)

#define __Pyx_long_cast(x) ((long)x)

#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\

    (sizeof(type) < sizeof(Py_ssize_t))  ||\

    (sizeof(type) > sizeof(Py_ssize_t) &&\

          likely(v < (type)PY_SSIZE_T_MAX ||\

                 v == (type)PY_SSIZE_T_MAX)  &&\

          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\

                                v == (type)PY_SSIZE_T_MIN)))  ||\

    (sizeof(type) == sizeof(Py_ssize_t) &&\

          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\

                               v == (type)PY_SSIZE_T_MAX)))  )

static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {

    return (size_t) i < (size_t) limit;

}

#if defined (__cplusplus) && __cplusplus >= 201103L

    #include <cstdlib>

    #define __Pyx_sst_abs(value) std::abs(value)

#elif SIZEOF_INT >= SIZEOF_SIZE_T

    #define __Pyx_sst_abs(value) abs(value)

#elif SIZEOF_LONG >= SIZEOF_SIZE_T

    #define __Pyx_sst_abs(value) labs(value)

#elif defined (_MSC_VER)

    #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))

#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L

    #define __Pyx_sst_abs(value) llabs(value)

#elif defined (__GNUC__)

    #define __Pyx_sst_abs(value) __builtin_llabs(value)

#else

    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)

#endif

static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);

static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);

#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))

#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)

#define __Pyx_PyBytes_FromString        PyBytes_FromString

#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize

static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);

#if PY_MAJOR_VERSION < 3

    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString

    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize

#else

    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString

    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize

#endif

#define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))

#define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AS_STRING(s))

#define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AS_STRING(s))

#define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AS_STRING(s))

#define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AS_STRING(s))

#define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AS_STRING(s))

#define __Pyx_PyObject_AsWritableString(s)    ((char*) __Pyx_PyObject_AsString(s))

#define __Pyx_PyObject_AsWritableSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))

#define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))

#define __Pyx_PyObject_AsSString(s)    ((const signed char*) __Pyx_PyObject_AsString(s))

#define __Pyx_PyObject_AsUString(s)    ((const unsigned char*) __Pyx_PyObject_AsString(s))

#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)

#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)

#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)

#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)

#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)

static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {

    const Py_UNICODE *u_end = u;

    while (*u_end++) ;

    return (size_t)(u_end - u - 1);

}

#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))

#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode

#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode

#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)

#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)

static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);

static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);

static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*);

static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);

#define __Pyx_PySequence_Tuple(obj)\

    (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))

static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);

static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);

#if CYTHON_ASSUME_SAFE_MACROS

#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))

#else

#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)

#endif

#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))

#if PY_MAJOR_VERSION >= 3

#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))

#else

#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))

#endif

#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))

#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII

static int __Pyx_sys_getdefaultencoding_not_ascii;

static int __Pyx_init_sys_getdefaultencoding_params(void) {

    PyObject* sys;

    PyObject* default_encoding = NULL;

    PyObject* ascii_chars_u = NULL;

    PyObject* ascii_chars_b = NULL;

    const char* default_encoding_c;

    sys = PyImport_ImportModule("sys");

    if (!sys) goto bad;

    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);

    Py_DECREF(sys);

    if (!default_encoding) goto bad;

    default_encoding_c = PyBytes_AsString(default_encoding);

    if (!default_encoding_c) goto bad;

    if (strcmp(default_encoding_c, "ascii") == 0) {

        __Pyx_sys_getdefaultencoding_not_ascii = 0;

    } else {

        char ascii_chars[128];

        int c;

        for (c = 0; c < 128; c++) {

            ascii_chars[c] = c;

        }

        __Pyx_sys_getdefaultencoding_not_ascii = 1;

        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);

        if (!ascii_chars_u) goto bad;

        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);

        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {

            PyErr_Format(

                PyExc_ValueError,

                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",

                default_encoding_c);

            goto bad;

        }

        Py_DECREF(ascii_chars_u);

        Py_DECREF(ascii_chars_b);

    }

    Py_DECREF(default_encoding);

    return 0;

bad:

    Py_XDECREF(default_encoding);

    Py_XDECREF(ascii_chars_u);

    Py_XDECREF(ascii_chars_b);

    return -1;

}

#endif

#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3

#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)

#else

#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)

#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT

static char* __PYX_DEFAULT_STRING_ENCODING;

static int __Pyx_init_sys_getdefaultencoding_params(void) {

    PyObject* sys;

    PyObject* default_encoding = NULL;

    char* default_encoding_c;

    sys = PyImport_ImportModule("sys");

    if (!sys) goto bad;

    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);

    Py_DECREF(sys);

    if (!default_encoding) goto bad;

    default_encoding_c = PyBytes_AsString(default_encoding);

    if (!default_encoding_c) goto bad;

    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1);

    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;

    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);

    Py_DECREF(default_encoding);

    return 0;

bad:

    Py_XDECREF(default_encoding);

    return -1;

}

#endif

#endif


/* Test for GCC > 2.95 */

#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))

  #define likely(x)   __builtin_expect(!!(x), 1)

  #define unlikely(x) __builtin_expect(!!(x), 0)

#else /* !__GNUC__ or GCC < 2.95 */

  #define likely(x)   (x)

  #define unlikely(x) (x)

#endif /* __GNUC__ */

static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }


static PyObject *__pyx_m = NULL;

static PyObject *__pyx_d;

static PyObject *__pyx_b;

static PyObject *__pyx_cython_runtime = NULL;

static PyObject *__pyx_empty_tuple;

static PyObject *__pyx_empty_bytes;

static PyObject *__pyx_empty_unicode;

static int __pyx_lineno;

static int __pyx_clineno = 0;

static const char * __pyx_cfilenm= __FILE__;

static const char *__pyx_filename;


/* Header.proto */

#if !defined(CYTHON_CCOMPLEX)

  #if defined(__cplusplus)

    #define CYTHON_CCOMPLEX 1

  #elif defined(_Complex_I)

    #define CYTHON_CCOMPLEX 1

  #else

    #define CYTHON_CCOMPLEX 0

  #endif

#endif

#if CYTHON_CCOMPLEX

  #ifdef __cplusplus

    #include <complex>

  #else

    #include <complex.h>

  #endif

#endif

#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)

  #undef _Complex_I

  #define _Complex_I 1.0fj

#endif


static const char *__pyx_f[] = {

  "proteus/subsurfaceTransportFunctions.pyx",

  "__init__.pxd",

  "type.pxd",

};

/* BufferFormatStructs.proto */

#define IS_UNSIGNED(type) (((type) -1) > 0)

struct __Pyx_StructField_;

#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)

typedef struct {

  const char* name;

  struct __Pyx_StructField_* fields;

  size_t size;

  size_t arraysize[8];

  int ndim;

  char typegroup;

  char is_unsigned;

  int flags;

} __Pyx_TypeInfo;

typedef struct __Pyx_StructField_ {

  __Pyx_TypeInfo* type;

  const char* name;

  size_t offset;

} __Pyx_StructField;

typedef struct {

  __Pyx_StructField* field;

  size_t parent_offset;

} __Pyx_BufFmt_StackElem;

typedef struct {

  __Pyx_StructField root;

  __Pyx_BufFmt_StackElem* head;

  size_t fmt_offset;

  size_t new_count, enc_count;

  size_t struct_alignment;

  int is_complex;

  char enc_type;

  char new_packmode;

  char enc_packmode;

  char is_valid_array;

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/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":697

 * # in Cython to enable them only on the right systems.

 *

 * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<

 * ctypedef npy_int16      int16_t

 * ctypedef npy_int32      int32_t

 */

typedef npy_int8 __pyx_t_5numpy_int8_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":698

 *

 * ctypedef npy_int8       int8_t

 * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<

 * ctypedef npy_int32      int32_t

 * ctypedef npy_int64      int64_t

 */

typedef npy_int16 __pyx_t_5numpy_int16_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":699

 * ctypedef npy_int8       int8_t

 * ctypedef npy_int16      int16_t

 * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<

 * ctypedef npy_int64      int64_t

 * #ctypedef npy_int96      int96_t

 */

typedef npy_int32 __pyx_t_5numpy_int32_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":700

 * ctypedef npy_int16      int16_t

 * ctypedef npy_int32      int32_t

 * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<

 * #ctypedef npy_int96      int96_t

 * #ctypedef npy_int128     int128_t

 */

typedef npy_int64 __pyx_t_5numpy_int64_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":704

 * #ctypedef npy_int128     int128_t

 *

 * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<

 * ctypedef npy_uint16     uint16_t

 * ctypedef npy_uint32     uint32_t

 */

typedef npy_uint8 __pyx_t_5numpy_uint8_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":705

 *

 * ctypedef npy_uint8      uint8_t

 * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<

 * ctypedef npy_uint32     uint32_t

 * ctypedef npy_uint64     uint64_t

 */

typedef npy_uint16 __pyx_t_5numpy_uint16_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":706

 * ctypedef npy_uint8      uint8_t

 * ctypedef npy_uint16     uint16_t

 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<

 * ctypedef npy_uint64     uint64_t

 * #ctypedef npy_uint96     uint96_t

 */

typedef npy_uint32 __pyx_t_5numpy_uint32_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":707

 * ctypedef npy_uint16     uint16_t

 * ctypedef npy_uint32     uint32_t

 * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<

 * #ctypedef npy_uint96     uint96_t

 * #ctypedef npy_uint128    uint128_t

 */

typedef npy_uint64 __pyx_t_5numpy_uint64_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":711

 * #ctypedef npy_uint128    uint128_t

 *

 * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<

 * ctypedef npy_float64    float64_t

 * #ctypedef npy_float80    float80_t

 */

typedef npy_float32 __pyx_t_5numpy_float32_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":712

 *

 * ctypedef npy_float32    float32_t

 * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<

 * #ctypedef npy_float80    float80_t

 * #ctypedef npy_float128   float128_t

 */

typedef npy_float64 __pyx_t_5numpy_float64_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":721

 * # The int types are mapped a bit surprising --

 * # numpy.int corresponds to 'l' and numpy.long to 'q'

 * ctypedef npy_long       int_t             # <<<<<<<<<<<<<<

 * ctypedef npy_longlong   long_t

 * ctypedef npy_longlong   longlong_t

 */

typedef npy_long __pyx_t_5numpy_int_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":722

 * # numpy.int corresponds to 'l' and numpy.long to 'q'

 * ctypedef npy_long       int_t

 * ctypedef npy_longlong   long_t             # <<<<<<<<<<<<<<

 * ctypedef npy_longlong   longlong_t

 *

 */

typedef npy_longlong __pyx_t_5numpy_long_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":723

 * ctypedef npy_long       int_t

 * ctypedef npy_longlong   long_t

 * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<

 *

 * ctypedef npy_ulong      uint_t

 */

typedef npy_longlong __pyx_t_5numpy_longlong_t;


/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":725

 * ctypedef npy_longlong   longlong_t

 *

 * ctypedef npy_ulong      uint_t             # <<<<<<<<<<<<<<

 * ctypedef npy_ulonglong  ulong_t

 * ctypedef npy_ulonglong  ulonglong_t

 */

typedef npy_ulong __pyx_t_5numpy_uint_t;


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/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":738

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/* "../miniconda3/envs/proteus-dev-up/lib/python3.8/site-packages/numpy/__init__.pxd":740

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#define __Pyx_PyObject_AsDouble(obj)\

(likely(PyFloat_CheckExact(obj)) ? PyFloat_AS_DOUBLE(obj) :\

 likely(PyInt_CheckExact(obj)) ?\

 PyFloat_AsDouble(obj) : __Pyx__PyObject_AsDouble(obj))

#else

#define __Pyx_PyObject_AsDouble(obj)\

((likely(PyFloat_CheckExact(obj))) ?\

 PyFloat_AS_DOUBLE(obj) : __Pyx__PyObject_AsDouble(obj))

#endif


/* RaiseTooManyValuesToUnpack.proto */

static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);


/* RaiseNeedMoreValuesToUnpack.proto */

static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);


/* RaiseNoneIterError.proto */

static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);


/* RaiseException.proto */

static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);


/* GetTopmostException.proto */

#if CYTHON_USE_EXC_INFO_STACK

static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate);

#endif


/* SaveResetException.proto */

#if CYTHON_FAST_THREAD_STATE

#define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)

static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);

#define __Pyx_ExceptionReset(type, value, tb)  __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)

static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);

#else

#define __Pyx_ExceptionSave(type, value, tb)   PyErr_GetExcInfo(type, value, tb)

#define __Pyx_ExceptionReset(type, value, tb)  PyErr_SetExcInfo(type, value, tb)

#endif


/* PyErrExceptionMatches.proto */

#if CYTHON_FAST_THREAD_STATE

#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)

static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);

#else

#define __Pyx_PyErr_ExceptionMatches(err)  PyErr_ExceptionMatches(err)

#endif


/* GetException.proto */

#if CYTHON_FAST_THREAD_STATE

#define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)

static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);

#else

static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);

#endif


/* TypeImport.proto */

#ifndef __PYX_HAVE_RT_ImportType_proto

#define __PYX_HAVE_RT_ImportType_proto

enum __Pyx_ImportType_CheckSize {

   __Pyx_ImportType_CheckSize_Error = 0,

   __Pyx_ImportType_CheckSize_Warn = 1,

   __Pyx_ImportType_CheckSize_Ignore = 2

};

static PyTypeObject *__Pyx_ImportType(PyObject* module, const char *module_name, const char *class_name, size_t size, enum __Pyx_ImportType_CheckSize check_size);

#endif


/* Import.proto */

static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);


/* CLineInTraceback.proto */

#ifdef CYTHON_CLINE_IN_TRACEBACK

#define __Pyx_CLineForTraceback(tstate, c_line)  (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)

#else

static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);

#endif


/* CodeObjectCache.proto */

typedef struct {

    PyCodeObject* code_object;

    int code_line;

} __Pyx_CodeObjectCacheEntry;

struct __Pyx_CodeObjectCache {

    int count;

    int max_count;

    __Pyx_CodeObjectCacheEntry* entries;

};

static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};

static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);

static PyCodeObject *__pyx_find_code_object(int code_line);

static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);


/* AddTraceback.proto */

static void __Pyx_AddTraceback(const char *funcname, int c_line,

                               int py_line, const char *filename);


/* BufferStructDeclare.proto */

typedef struct {

  Py_ssize_t shape, strides, suboffsets;

} __Pyx_Buf_DimInfo;

typedef struct {

  size_t refcount;

  Py_buffer pybuffer;

} __Pyx_Buffer;

typedef struct {

  __Pyx_Buffer *rcbuffer;

  char *data;

  __Pyx_Buf_DimInfo diminfo[8];

} __Pyx_LocalBuf_ND;


#if PY_MAJOR_VERSION < 3

    static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);

    static void __Pyx_ReleaseBuffer(Py_buffer *view);

#else

    #define __Pyx_GetBuffer PyObject_GetBuffer

    #define __Pyx_ReleaseBuffer PyBuffer_Release

#endif


/* CIntToPy.proto */

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);


/* CIntToPy.proto */

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_Py_intptr_t(Py_intptr_t value);


/* CIntToPy.proto */

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);


/* RealImag.proto */

#if CYTHON_CCOMPLEX

  #ifdef __cplusplus

    #define __Pyx_CREAL(z) ((z).real())

    #define __Pyx_CIMAG(z) ((z).imag())

  #else

    #define __Pyx_CREAL(z) (__real__(z))

    #define __Pyx_CIMAG(z) (__imag__(z))

  #endif

#else

    #define __Pyx_CREAL(z) ((z).real)

    #define __Pyx_CIMAG(z) ((z).imag)

#endif

#if defined(__cplusplus) && CYTHON_CCOMPLEX\

        && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103)

    #define __Pyx_SET_CREAL(z,x) ((z).real(x))

    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))

#else

    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)

    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)

#endif


/* Arithmetic.proto */

#if CYTHON_CCOMPLEX

    #define __Pyx_c_eq_float(a, b)   ((a)==(b))

    #define __Pyx_c_sum_float(a, b)  ((a)+(b))

    #define __Pyx_c_diff_float(a, b) ((a)-(b))

    #define __Pyx_c_prod_float(a, b) ((a)*(b))

    #define __Pyx_c_quot_float(a, b) ((a)/(b))

    #define __Pyx_c_neg_float(a)     (-(a))

  #ifdef __cplusplus

    #define __Pyx_c_is_zero_float(z) ((z)==(float)0)

    #define __Pyx_c_conj_float(z)    (::std::conj(z))

    #if 1

        #define __Pyx_c_abs_float(z)     (::std::abs(z))

        #define __Pyx_c_pow_float(a, b)  (::std::pow(a, b))

    #endif

  #else

    #define __Pyx_c_is_zero_float(z) ((z)==0)

    #define __Pyx_c_conj_float(z)    (conjf(z))

    #if 1

        #define __Pyx_c_abs_float(z)     (cabsf(z))

        #define __Pyx_c_pow_float(a, b)  (cpowf(a, b))

    #endif

 #endif

#else

    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex);

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex);

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex);

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex);

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex);

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex);

    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex);

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex);

    #if 1

        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex);

        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex);

    #endif

#endif


/* Arithmetic.proto */

#if CYTHON_CCOMPLEX

    #define __Pyx_c_eq_double(a, b)   ((a)==(b))

    #define __Pyx_c_sum_double(a, b)  ((a)+(b))

    #define __Pyx_c_diff_double(a, b) ((a)-(b))

    #define __Pyx_c_prod_double(a, b) ((a)*(b))

    #define __Pyx_c_quot_double(a, b) ((a)/(b))

    #define __Pyx_c_neg_double(a)     (-(a))

  #ifdef __cplusplus

    #define __Pyx_c_is_zero_double(z) ((z)==(double)0)

    #define __Pyx_c_conj_double(z)    (::std::conj(z))

    #if 1

        #define __Pyx_c_abs_double(z)     (::std::abs(z))

        #define __Pyx_c_pow_double(a, b)  (::std::pow(a, b))

    #endif

  #else

    #define __Pyx_c_is_zero_double(z) ((z)==0)

    #define __Pyx_c_conj_double(z)    (conj(z))

    #if 1

        #define __Pyx_c_abs_double(z)     (cabs(z))

        #define __Pyx_c_pow_double(a, b)  (cpow(a, b))

    #endif

 #endif

#else

    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex);

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex);

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex);

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex);

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex);

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex);

    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex);

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex);

    #if 1

        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex);

        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex);

    #endif

#endif


/* CIntToPy.proto */

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value);


/* CIntFromPy.proto */

static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);


/* CIntFromPy.proto */

static CYTHON_INLINE Py_intptr_t __Pyx_PyInt_As_Py_intptr_t(PyObject *);


/* CIntFromPy.proto */

static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);


/* FastTypeChecks.proto */

#if CYTHON_COMPILING_IN_CPYTHON

#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)

static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);

static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);

static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);

#else

#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)

#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)

#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))

#endif

#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)


/* CheckBinaryVersion.proto */

static int __Pyx_check_binary_version(void);


/* InitStrings.proto */

static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);


/* Module declarations from 'cpython.buffer' */


/* Module declarations from 'libc.string' */


/* Module declarations from 'libc.stdio' */


/* Module declarations from '__builtin__' */


/* Module declarations from 'cpython.type' */

static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;


/* Module declarations from 'cpython' */


/* Module declarations from 'cpython.object' */


/* Module declarations from 'cpython.ref' */


/* Module declarations from 'cpython.mem' */


/* Module declarations from 'numpy' */


/* Module declarations from 'numpy' */

static PyTypeObject *__pyx_ptype_5numpy_dtype = 0;

static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0;

static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0;

static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0;

static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0;

static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, char *, char *, int *); /*proto*/


/* Module declarations from 'subsurfaceTransportFunctions' */

static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_28subsurfaceTransportFunctions_ITYPE_t = { "ITYPE_t", NULL, sizeof(__pyx_t_28subsurfaceTransportFunctions_ITYPE_t), { 0 }, 0, IS_UNSIGNED(__pyx_t_28subsurfaceTransportFunctions_ITYPE_t) ? 'U' : 'I', IS_UNSIGNED(__pyx_t_28subsurfaceTransportFunctions_ITYPE_t), 0 };

static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_28subsurfaceTransportFunctions_DTYPE_t = { "DTYPE_t", NULL, sizeof(__pyx_t_28subsurfaceTransportFunctions_DTYPE_t), { 0 }, 0, 'R', 0, 0 };

#define __Pyx_MODULE_NAME "subsurfaceTransportFunctions"

extern int __pyx_module_is_main_subsurfaceTransportFunctions;

int __pyx_module_is_main_subsurfaceTransportFunctions = 0;


/* Implementation of 'subsurfaceTransportFunctions' */

static PyObject *__pyx_builtin_range;

static PyObject *__pyx_builtin_RuntimeError;

static PyObject *__pyx_builtin_ValueError;

static PyObject *__pyx_builtin_ImportError;

static const char __pyx_k_I[] = "I";

static const char __pyx_k_J[] = "J";

static const char __pyx_k_d[] = "d";

static const char __pyx_k_i[] = "i";

static const char __pyx_k_j[] = "j";

static const char __pyx_k_k[] = "k";

static const char __pyx_k_m[] = "m";

static const char __pyx_k_n[] = "n";

static const char __pyx_k_q[] = "q";

static const char __pyx_k_t[] = "t";

static const char __pyx_k_v[] = "v";

static const char __pyx_k_w[] = "w";

static const char __pyx_k_x[] = "x";

static const char __pyx_k_dS[] = "dS";

static const char __pyx_k_dV[] = "dV";

static const char __pyx_k_df[] = "df";

static const char __pyx_k_dm[] = "dm";

static const char __pyx_k_eN[] = "eN";

static const char __pyx_k_ii[] = "ii";

static const char __pyx_k_kb[] = "kb";

static const char __pyx_k_mt[] = "mt";

static const char __pyx_k_nd[] = "nd";

static const char __pyx_k_pi[] = "pi";

static const char __pyx_k_xc[] = "xc";

static const char __pyx_k_yc[] = "yc";

static const char __pyx_k_KWr[] = "KWr";

static const char __pyx_k_KWs[] = "KWs";

static const char __pyx_k_dmt[] = "dmt";

static const char __pyx_k_dot[] = "dot";

static const char __pyx_k_ebN[] = "ebN";

static const char __pyx_k_l2g[] = "l2g";

static const char __pyx_k_nnz[] = "nnz";

static const char __pyx_k_q_m[] = "q_m";

static const char __pyx_k_q_r[] = "q_r";

static const char __pyx_k_q_u[] = "q_u";

static const char __pyx_k_q_x[] = "q_x";

static const char __pyx_k_rho[] = "rho";

static const char __pyx_k_sum[] = "sum";

static const char __pyx_k_u_j[] = "u_j";

static const char __pyx_k_vol[] = "vol";

static const char __pyx_k_a_eN[] = "a_eN";

static const char __pyx_k_a_up[] = "a_up";

static const char __pyx_k_beta[] = "beta";

static const char __pyx_k_ebNE[] = "ebNE";

static const char __pyx_k_f_up[] = "f_up";

static const char __pyx_k_flat[] = "flat";

static const char __pyx_k_flux[] = "flux";

static const char __pyx_k_main[] = "__main__";

static const char __pyx_k_name[] = "__name__";

static const char __pyx_k_one8[] = "one8";

static const char __pyx_k_psiC[] = "psiC";

static const char __pyx_k_q_dm[] = "q_dm";

static const char __pyx_k_q_kr[] = "q_kr";

static const char __pyx_k_q_mt[] = "q_mt";

static const char __pyx_k_rho2[] = "rho2";

static const char __pyx_k_rhom[] = "rhom";

static const char __pyx_k_sBar[] = "sBar";

static const char __pyx_k_test[] = "__test__";

static const char __pyx_k_u_eN[] = "u_eN";

static const char __pyx_k_vBar[] = "vBar";

static const char __pyx_k_a_avg[] = "a_avg";

static const char __pyx_k_alpha[] = "alpha";

static const char __pyx_k_clock[] = "clock";

static const char __pyx_k_denom[] = "denom";

static const char __pyx_k_drhom[] = "drhom";

static const char __pyx_k_kr_eN[] = "kr_eN";

static const char __pyx_k_matID[] = "matID";

static const char __pyx_k_numer[] = "numer";

static const char __pyx_k_numpy[] = "numpy";

static const char __pyx_k_pcBar[] = "pcBar";

static const char __pyx_k_q_dkr[] = "q_dkr";

static const char __pyx_k_q_dmt[] = "q_dmt";

static const char __pyx_k_range[] = "range";

static const char __pyx_k_shape[] = "shape";

static const char __pyx_k_u_dof[] = "u_dof";

static const char __pyx_k_u_l2g[] = "u_l2g";

static const char __pyx_k_vBar2[] = "vBar2";

static const char __pyx_k_vol_e[] = "vol_e";

static const char __pyx_k_zeros[] = "zeros";

static const char __pyx_k_a_neig[] = "a_neig";

static const char __pyx_k_colind[] = "colind";

static const char __pyx_k_dkr_up[] = "dkr_up";

static const char __pyx_k_import[] = "__import__";

static const char __pyx_k_mt_avg[] = "mt_avg";

static const char __pyx_k_nSpace[] = "nSpace";

static const char __pyx_k_phi_eN[] = "phi_eN";

static const char __pyx_k_picard[] = "picard";

static const char __pyx_k_q_alin[] = "q_alin";

static const char __pyx_k_q_detJ[] = "q_detJ";

static const char __pyx_k_q_flin[] = "q_flin";

static const char __pyx_k_q_mass[] = "q_mass";

static const char __pyx_k_q_vals[] = "q_vals";

static const char __pyx_k_rowptr[] = "rowptr";

static const char __pyx_k_thetaR[] = "thetaR";

static const char __pyx_k_thetaS[] = "thetaS";

static const char __pyx_k_thetaW[] = "thetaW";

static const char __pyx_k_u_neig[] = "u_neig";

static const char __pyx_k_volume[] = "volume";

static const char __pyx_k_weight[] = "weight";

static const char __pyx_k_df_dofs[] = "df_dofs";

static const char __pyx_k_eN_left[] = "eN_left";

static const char __pyx_k_gravity[] = "gravity";

static const char __pyx_k_kr_neig[] = "kr_neig";

static const char __pyx_k_nSpace2[] = "nSpace2";

static const char __pyx_k_omega_e[] = "omega_e";

static const char __pyx_k_pcBar_n[] = "pcBar_n";

static const char __pyx_k_q_dmass[] = "q_dmass";

static const char __pyx_k_q_kr_up[] = "q_kr_up";

static const char __pyx_k_thetaSR[] = "thetaSR";

static const char __pyx_k_dmtj_avg[] = "dmtj_avg";

static const char __pyx_k_eN_right[] = "eN_right";

static const char __pyx_k_ebq_vals[] = "ebq_vals";

static const char __pyx_k_integral[] = "integral";

static const char __pyx_k_material[] = "material";

static const char __pyx_k_phi_neig[] = "phi_neig";

static const char __pyx_k_q_grad_u[] = "q_grad_u";

static const char __pyx_k_q_grad_v[] = "q_grad_v";

static const char __pyx_k_q_grad_w[] = "q_grad_w";

static const char __pyx_k_ebN_local[] = "ebN_local";

static const char __pyx_k_pcBar_nM1[] = "pcBar_nM1";

static const char __pyx_k_pcBar_nM2[] = "pcBar_nM2";

static const char __pyx_k_sqrt_sBar[] = "sqrt_sBar";

static const char __pyx_k_transient[] = "transient";

static const char __pyx_k_volFactor[] = "volFactor";

static const char __pyx_k_zVelocity[] = "zVelocity";

static const char __pyx_k_zvelocity[] = "zvelocity";

static const char __pyx_k_DKWr_DpsiC[] = "DKWr_DpsiC";

static const char __pyx_k_ValueError[] = "ValueError";

static const char __pyx_k_matID_neig[] = "matID_neig";

static const char __pyx_k_nAvgWeight[] = "nAvgWeight";

static const char __pyx_k_upwindFlag[] = "upwindFlag";

static const char __pyx_k_DsBar_DpsiC[] = "DsBar_DpsiC";

static const char __pyx_k_DvBar_DpsiC[] = "DvBar_DpsiC";

static const char __pyx_k_ImportError[] = "ImportError";

static const char __pyx_k_eN_neighbor[] = "eN_neighbor";

static const char __pyx_k_RuntimeError[] = "RuntimeError";

static const char __pyx_k_tForReversal[] = "tForReversal";

static const char __pyx_k_DthetaW_DpsiC[] = "DthetaW_DpsiC";

static const char __pyx_k_material_left[] = "material_left";

static const char __pyx_k_weak_residual[] = "weak_residual";

static const char __pyx_k_material_right[] = "material_right";

static const char __pyx_k_ebq_global_vals[] = "ebq_global_vals";

static const char __pyx_k_elementJacobian[] = "elementJacobian";

static const char __pyx_k_elementResidual[] = "elementResidual";

static const char __pyx_k_onePlus_pcBar_n[] = "onePlus_pcBar_n";

static const char __pyx_k_nElements_global[] = "nElements_global";

static const char __pyx_k_nDOF_test_element[] = "nDOF_test_element";

static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";

static const char __pyx_k_material_functions[] = "material_functions";

static const char __pyx_k_nDOF_trial_element[] = "nDOF_trial_element";

static const char __pyx_k_updateMass_weakAvg[] = "updateMass_weakAvg";

static const char __pyx_k_calculateNormalFlux[] = "calculateNormalFlux";

static const char __pyx_k_thisElementIsUpwind[] = "thisElementIsUpwind";

static const char __pyx_k_elementBoundaryTypes[] = "elementBoundaryTypes";

static const char __pyx_k_elementMaterialTypes[] = "elementMaterialTypes";

static const char __pyx_k_elementNeighborsArray[] = "elementNeighborsArray";

static const char __pyx_k_elementBoundariesArray[] = "elementBoundariesArray";

static const char __pyx_k_jacobian_weak_residual[] = "jacobian_weak_residual";

static const char __pyx_k_characteristic_velocity[] = "characteristic_velocity";

static const char __pyx_k_elementBarycentersArray[] = "elementBarycentersArray";

static const char __pyx_k_nElementBoundaries_global[] = "nElementBoundaries_global";

static const char __pyx_k_setElementBoundariesArray[] = "setElementBoundariesArray";

static const char __pyx_k_RE_NCP1_getElementJacobian[] = "RE_NCP1_getElementJacobian";

static const char __pyx_k_RE_NCP1_getElementResidual[] = "RE_NCP1_getElementResidual";

static const char __pyx_k_nElementBoundaries_element[] = "nElementBoundaries_element";

static const char __pyx_k_updateMassJacobian_weakAvg[] = "updateMassJacobian_weakAvg";

static const char __pyx_k_vortexElementVelocityEval3[] = "vortexElementVelocityEval3";

static const char __pyx_k_vortexElementVelocityEval4[] = "vortexElementVelocityEval4";

static const char __pyx_k_helicalElementVelocityEval3[] = "helicalElementVelocityEval3";

static const char __pyx_k_helicalElementVelocityEval4[] = "helicalElementVelocityEval4";

static const char __pyx_k_characteristic_velocity_dofs[] = "characteristic_velocity_dofs";

static const char __pyx_k_elementBoundaryElementsArray[] = "elementBoundaryElementsArray";

static const char __pyx_k_elementBoundaryMaterialTypes[] = "elementBoundaryMaterialTypes";

static const char __pyx_k_subsurfaceTransportFunctions[] = "subsurfaceTransportFunctions";

static const char __pyx_k_exteriorElementBoundariesArray[] = "exteriorElementBoundariesArray";

static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import";

static const char __pyx_k_setExteriorElementBoundaryTypes[] = "setExteriorElementBoundaryTypes";

static const char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";

static const char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";

static const char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";

static const char __pyx_k_RE_NCP1_evaluateElementCoefficie[] = "RE_NCP1_evaluateElementCoefficients_Linear";

static const char __pyx_k_computeSimpleCharacteristicVeloc[] = "computeSimpleCharacteristicVelocityFromElementVelocity";

static const char __pyx_k_evaluateScalarMaterialFunctionOv[] = "evaluateScalarMaterialFunctionOverElements";

static const char __pyx_k_evaluateSparseTensorMaterialFunc[] = "evaluateSparseTensorMaterialFunctionOverElementBoundaries_harmonicAverage";

static const char __pyx_k_evaluateVectorMaterialFunctionOv[] = "evaluateVectorMaterialFunctionOverElements";

static const char __pyx_k_exteriorElementBoundaryMaterialT[] = "exteriorElementBoundaryMaterialTypes";

static const char __pyx_k_nExteriorElementBoundaries_globa[] = "nExteriorElementBoundaries_global";

static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import";

static const char __pyx_k_proteus_subsurfaceTransportFunct[] = "proteus/subsurfaceTransportFunctions.pyx";

static const char __pyx_k_rotatingGaussianElementVelocityE[] = "rotatingGaussianElementVelocityEval3";

static const char __pyx_k_setScalarMaterialFunctionOverEle[] = "setScalarMaterialFunctionOverElements";

static const char __pyx_k_setScalarMaterialFunctionOverGlo[] = "setScalarMaterialFunctionOverGlobalElementBoundaries_arithmeticAverage";

static const char __pyx_k_setSparseTensorMaterialFunctionO[] = "setSparseTensorMaterialFunctionOverElementBoundaries_harmonicAverage";

static const char __pyx_k_setVectorMaterialFunctionOverEle[] = "setVectorMaterialFunctionOverElements";

static const char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";

static const char __pyx_k_RE_NCP1_evaluateElementCoefficie_2[] = "RE_NCP1_evaluateElementCoefficients_VGM";

static const char __pyx_k_computeSimpleCharacteristicVeloc_2[] = "computeSimpleCharacteristicVelocityFromVelocityDOFs";

static const char __pyx_k_evaluateScalarMaterialFunctionOv_2[] = "evaluateScalarMaterialFunctionOverElementBoundaries_arithmeticAverage";

static const char __pyx_k_evaluateScalarMaterialFunctionOv_3[] = "evaluateScalarMaterialFunctionOverGlobalElementBoundaries_arithmeticAverage";

static const char __pyx_k_evaluateSparseTensorMaterialFunc_2[] = "evaluateSparseTensorMaterialFunctionOverGlobalElementBoundaries_harmonicAverage";

static const char __pyx_k_rotatingGaussianElementVelocityE_2[] = "rotatingGaussianElementVelocityEval4";

static const char __pyx_k_setScalarMaterialFunctionOverEle_2[] = "setScalarMaterialFunctionOverElementBoundaries_arithmeticAverage";

static const char __pyx_k_setSparseTensorMaterialFunctionO_2[] = "setSparseTensorMaterialFunctionOverGlobalElementBoundaries_harmonicAverage";

static PyObject *__pyx_n_s_DKWr_DpsiC;

static PyObject *__pyx_n_s_DsBar_DpsiC;

static PyObject *__pyx_n_s_DthetaW_DpsiC;

static PyObject *__pyx_n_s_DvBar_DpsiC;

static PyObject *__pyx_kp_u_Format_string_allocated_too_shor;

static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2;

static PyObject *__pyx_n_s_I;

static PyObject *__pyx_n_s_ImportError;

static PyObject *__pyx_n_s_J;

static PyObject *__pyx_n_s_KWr;

static PyObject *__pyx_n_s_KWs;

static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;

static PyObject *__pyx_n_s_RE_NCP1_evaluateElementCoefficie;

static PyObject *__pyx_n_s_RE_NCP1_evaluateElementCoefficie_2;

static PyObject *__pyx_n_s_RE_NCP1_getElementJacobian;

static PyObject *__pyx_n_s_RE_NCP1_getElementResidual;

static PyObject *__pyx_n_s_RuntimeError;

static PyObject *__pyx_n_s_ValueError;

static PyObject *__pyx_n_s_a_avg;

static PyObject *__pyx_n_s_a_eN;

static PyObject *__pyx_n_s_a_neig;

static PyObject *__pyx_n_s_a_up;

static PyObject *__pyx_n_s_alpha;

static PyObject *__pyx_n_s_beta;

static PyObject *__pyx_n_s_calculateNormalFlux;

static PyObject *__pyx_n_s_characteristic_velocity;

static PyObject *__pyx_n_s_characteristic_velocity_dofs;

static PyObject *__pyx_n_s_cline_in_traceback;

static PyObject *__pyx_n_s_clock;

static PyObject *__pyx_n_s_colind;

static PyObject *__pyx_n_s_computeSimpleCharacteristicVeloc;

static PyObject *__pyx_n_s_computeSimpleCharacteristicVeloc_2;

static PyObject *__pyx_n_s_d;

static PyObject *__pyx_n_s_dS;

static PyObject *__pyx_n_s_dV;

static PyObject *__pyx_n_s_denom;

static PyObject *__pyx_n_s_df;

static PyObject *__pyx_n_s_df_dofs;

static PyObject *__pyx_n_s_dkr_up;

static PyObject *__pyx_n_s_dm;

static PyObject *__pyx_n_s_dmt;

static PyObject *__pyx_n_s_dmtj_avg;

static PyObject *__pyx_n_s_dot;

static PyObject *__pyx_n_s_drhom;

static PyObject *__pyx_n_s_eN;

static PyObject *__pyx_n_s_eN_left;

static PyObject *__pyx_n_s_eN_neighbor;

static PyObject *__pyx_n_s_eN_right;

static PyObject *__pyx_n_s_ebN;

static PyObject *__pyx_n_s_ebNE;

static PyObject *__pyx_n_s_ebN_local;

static PyObject *__pyx_n_s_ebq_global_vals;

static PyObject *__pyx_n_s_ebq_vals;

static PyObject *__pyx_n_s_elementBarycentersArray;

static PyObject *__pyx_n_s_elementBoundariesArray;

static PyObject *__pyx_n_s_elementBoundaryElementsArray;

static PyObject *__pyx_n_s_elementBoundaryMaterialTypes;

static PyObject *__pyx_n_s_elementBoundaryTypes;

static PyObject *__pyx_n_s_elementJacobian;

static PyObject *__pyx_n_s_elementMaterialTypes;

static PyObject *__pyx_n_s_elementNeighborsArray;

static PyObject *__pyx_n_s_elementResidual;

static PyObject *__pyx_n_s_evaluateScalarMaterialFunctionOv;

static PyObject *__pyx_n_s_evaluateScalarMaterialFunctionOv_2;

static PyObject *__pyx_n_s_evaluateScalarMaterialFunctionOv_3;

static PyObject *__pyx_n_s_evaluateSparseTensorMaterialFunc;

static PyObject *__pyx_n_s_evaluateSparseTensorMaterialFunc_2;

static PyObject *__pyx_n_s_evaluateVectorMaterialFunctionOv;

static PyObject *__pyx_n_s_exteriorElementBoundariesArray;

static PyObject *__pyx_n_s_exteriorElementBoundaryMaterialT;

static PyObject *__pyx_n_s_f_up;

static PyObject *__pyx_n_s_flat;

static PyObject *__pyx_n_s_flux;

static PyObject *__pyx_n_s_gravity;

static PyObject *__pyx_n_s_helicalElementVelocityEval3;

static PyObject *__pyx_n_s_helicalElementVelocityEval4;

static PyObject *__pyx_n_s_i;

static PyObject *__pyx_n_s_ii;

static PyObject *__pyx_n_s_import;

static PyObject *__pyx_n_s_integral;

static PyObject *__pyx_n_s_j;

static PyObject *__pyx_n_s_jacobian_weak_residual;

static PyObject *__pyx_n_s_k;

static PyObject *__pyx_n_s_kb;

static PyObject *__pyx_n_s_kr_eN;

static PyObject *__pyx_n_s_kr_neig;

static PyObject *__pyx_n_s_l2g;

static PyObject *__pyx_n_s_m;

static PyObject *__pyx_n_s_main;

static PyObject *__pyx_n_s_matID;

static PyObject *__pyx_n_s_matID_neig;

static PyObject *__pyx_n_s_material;

static PyObject *__pyx_n_s_material_functions;

static PyObject *__pyx_n_s_material_left;

static PyObject *__pyx_n_s_material_right;

static PyObject *__pyx_n_s_mt;

static PyObject *__pyx_n_s_mt_avg;

static PyObject *__pyx_n_s_n;

static PyObject *__pyx_n_s_nAvgWeight;

static PyObject *__pyx_n_s_nDOF_test_element;

static PyObject *__pyx_n_s_nDOF_trial_element;

static PyObject *__pyx_n_s_nElementBoundaries_element;

static PyObject *__pyx_n_s_nElementBoundaries_global;

static PyObject *__pyx_n_s_nElements_global;

static PyObject *__pyx_n_s_nExteriorElementBoundaries_globa;

static PyObject *__pyx_n_s_nSpace;

static PyObject *__pyx_n_s_nSpace2;

static PyObject *__pyx_n_s_name;

static PyObject *__pyx_n_s_nd;

static PyObject *__pyx_n_s_nnz;

static PyObject *__pyx_n_s_numer;

static PyObject *__pyx_n_s_numpy;

static PyObject *__pyx_kp_s_numpy_core_multiarray_failed_to;

static PyObject *__pyx_kp_s_numpy_core_umath_failed_to_impor;

static PyObject *__pyx_n_s_omega_e;

static PyObject *__pyx_n_s_one8;

static PyObject *__pyx_n_s_onePlus_pcBar_n;

static PyObject *__pyx_n_s_pcBar;

static PyObject *__pyx_n_s_pcBar_n;

static PyObject *__pyx_n_s_pcBar_nM1;

static PyObject *__pyx_n_s_pcBar_nM2;

static PyObject *__pyx_n_s_phi_eN;

static PyObject *__pyx_n_s_phi_neig;

static PyObject *__pyx_n_s_pi;

static PyObject *__pyx_n_s_picard;

static PyObject *__pyx_kp_s_proteus_subsurfaceTransportFunct;

static PyObject *__pyx_n_s_psiC;

static PyObject *__pyx_n_s_q;

static PyObject *__pyx_n_s_q_alin;

static PyObject *__pyx_n_s_q_detJ;

static PyObject *__pyx_n_s_q_dkr;

static PyObject *__pyx_n_s_q_dm;

static PyObject *__pyx_n_s_q_dmass;

static PyObject *__pyx_n_s_q_dmt;

static PyObject *__pyx_n_s_q_flin;

static PyObject *__pyx_n_s_q_grad_u;

static PyObject *__pyx_n_s_q_grad_v;

static PyObject *__pyx_n_s_q_grad_w;

static PyObject *__pyx_n_s_q_kr;

static PyObject *__pyx_n_s_q_kr_up;

static PyObject *__pyx_n_s_q_m;

static PyObject *__pyx_n_s_q_mass;

static PyObject *__pyx_n_s_q_mt;

static PyObject *__pyx_n_s_q_r;

static PyObject *__pyx_n_s_q_u;

static PyObject *__pyx_n_s_q_vals;

static PyObject *__pyx_n_s_q_x;

static PyObject *__pyx_n_s_range;

static PyObject *__pyx_n_s_rho;

static PyObject *__pyx_n_s_rho2;

static PyObject *__pyx_n_s_rhom;

static PyObject *__pyx_n_s_rotatingGaussianElementVelocityE;

static PyObject *__pyx_n_s_rotatingGaussianElementVelocityE_2;

static PyObject *__pyx_n_s_rowptr;

static PyObject *__pyx_n_s_sBar;

static PyObject *__pyx_n_s_setElementBoundariesArray;

static PyObject *__pyx_n_s_setExteriorElementBoundaryTypes;

static PyObject *__pyx_n_s_setScalarMaterialFunctionOverEle;

static PyObject *__pyx_n_s_setScalarMaterialFunctionOverEle_2;

static PyObject *__pyx_n_s_setScalarMaterialFunctionOverGlo;

static PyObject *__pyx_n_s_setSparseTensorMaterialFunctionO;

static PyObject *__pyx_n_s_setSparseTensorMaterialFunctionO_2;

static PyObject *__pyx_n_s_setVectorMaterialFunctionOverEle;

static PyObject *__pyx_n_s_shape;

static PyObject *__pyx_n_s_sqrt_sBar;

static PyObject *__pyx_n_s_subsurfaceTransportFunctions;

static PyObject *__pyx_n_s_sum;

static PyObject *__pyx_n_s_t;

static PyObject *__pyx_n_s_tForReversal;

static PyObject *__pyx_n_s_test;

static PyObject *__pyx_n_s_thetaR;

static PyObject *__pyx_n_s_thetaS;

static PyObject *__pyx_n_s_thetaSR;

static PyObject *__pyx_n_s_thetaW;

static PyObject *__pyx_n_s_thisElementIsUpwind;

static PyObject *__pyx_n_s_transient;

static PyObject *__pyx_n_s_u_dof;

static PyObject *__pyx_n_s_u_eN;

static PyObject *__pyx_n_s_u_j;

static PyObject *__pyx_n_s_u_l2g;

static PyObject *__pyx_n_s_u_neig;

static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;

static PyObject *__pyx_n_s_updateMassJacobian_weakAvg;

static PyObject *__pyx_n_s_updateMass_weakAvg;

static PyObject *__pyx_n_s_upwindFlag;

static PyObject *__pyx_n_s_v;

static PyObject *__pyx_n_s_vBar;

static PyObject *__pyx_n_s_vBar2;

static PyObject *__pyx_n_s_vol;

static PyObject *__pyx_n_s_volFactor;

static PyObject *__pyx_n_s_vol_e;

static PyObject *__pyx_n_s_volume;

static PyObject *__pyx_n_s_vortexElementVelocityEval3;

static PyObject *__pyx_n_s_vortexElementVelocityEval4;

static PyObject *__pyx_n_s_w;

static PyObject *__pyx_n_s_weak_residual;

static PyObject *__pyx_n_s_weight;

static PyObject *__pyx_n_s_x;

static PyObject *__pyx_n_s_xc;

static PyObject *__pyx_n_s_yc;

static PyObject *__pyx_n_s_zVelocity;

static PyObject *__pyx_n_s_zeros;

static PyObject *__pyx_n_s_zvelocity;

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_setExteriorElementBoundaryTypes(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_nExteriorElementBoundaries_global, PyArrayObject *__pyx_v_exteriorElementBoundariesArray, PyArrayObject *__pyx_v_elementBoundaryElementsArray, PyArrayObject *__pyx_v_elementMaterialTypes, PyArrayObject *__pyx_v_exteriorElementBoundaryMaterialTypes); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_2setElementBoundariesArray(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_nElementBoundaries_global, PyArrayObject *__pyx_v_elementBoundaryElementsArray, PyArrayObject *__pyx_v_elementMaterialTypes, PyArrayObject *__pyx_v_elementBoundaryMaterialTypes); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_4setScalarMaterialFunctionOverElements(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_elementMaterialTypes, PyArrayObject *__pyx_v_q_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_6setVectorMaterialFunctionOverElements(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_elementMaterialTypes, PyArrayObject *__pyx_v_q_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_8setScalarMaterialFunctionOverElementBoundaries_arithmeticAverage(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_elementBoundariesArray, PyArrayObject *__pyx_v_elementBoundaryTypes, PyArrayObject *__pyx_v_ebq_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_10setSparseTensorMaterialFunctionOverElementBoundaries_harmonicAverage(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_nd, PyArrayObject *__pyx_v_elementBoundariesArray, PyArrayObject *__pyx_v_elementBoundaryTypes, PyArrayObject *__pyx_v_ebq_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_12setScalarMaterialFunctionOverGlobalElementBoundaries_arithmeticAverage(CYTHON_UNUSED PyObject *__pyx_self, CYTHON_UNUSED PyArrayObject *__pyx_v_elementBoundariesArray, PyArrayObject *__pyx_v_elementBoundaryTypes, PyArrayObject *__pyx_v_ebq_global_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_14setSparseTensorMaterialFunctionOverGlobalElementBoundaries_harmonicAverage(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_nd, CYTHON_UNUSED PyArrayObject *__pyx_v_elementBoundariesArray, PyArrayObject *__pyx_v_elementBoundaryTypes, PyArrayObject *__pyx_v_ebq_global_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_16evaluateScalarMaterialFunctionOverElements(CYTHON_UNUSED PyObject *__pyx_self, double __pyx_v_t, PyArrayObject *__pyx_v_elementMaterialTypes, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_q_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_18evaluateVectorMaterialFunctionOverElements(CYTHON_UNUSED PyObject *__pyx_self, double __pyx_v_t, PyArrayObject *__pyx_v_elementMaterialTypes, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_q_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_20evaluateScalarMaterialFunctionOverElementBoundaries_arithmeticAverage(CYTHON_UNUSED PyObject *__pyx_self, double __pyx_v_t, PyArrayObject *__pyx_v_elementBoundariesArray, PyArrayObject *__pyx_v_elementBoundaryTypes, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_ebq_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_22evaluateSparseTensorMaterialFunctionOverElementBoundaries_harmonicAverage(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_nd, double __pyx_v_t, PyArrayObject *__pyx_v_elementBoundariesArray, PyArrayObject *__pyx_v_elementBoundaryTypes, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_ebq_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_24evaluateScalarMaterialFunctionOverGlobalElementBoundaries_arithmeticAverage(CYTHON_UNUSED PyObject *__pyx_self, double __pyx_v_t, CYTHON_UNUSED PyArrayObject *__pyx_v_elementBoundariesArray, PyArrayObject *__pyx_v_elementBoundaryTypes, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_ebq_global_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_26evaluateSparseTensorMaterialFunctionOverGlobalElementBoundaries_harmonicAverage(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_nd, double __pyx_v_t, CYTHON_UNUSED PyArrayObject *__pyx_v_elementBoundariesArray, PyArrayObject *__pyx_v_elementBoundaryTypes, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_ebq_global_vals, PyObject *__pyx_v_material_functions); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_28RE_NCP1_evaluateElementCoefficients_Linear(CYTHON_UNUSED PyObject *__pyx_self, double __pyx_v_rho, PyArrayObject *__pyx_v_gravity, PyArrayObject *__pyx_v_rowptr, PyArrayObject *__pyx_v_colind, PyArrayObject *__pyx_v_KWs, int __pyx_v_nSpace, int __pyx_v_nElements_global, int __pyx_v_nElementBoundaries_element, PyArrayObject *__pyx_v_elementNeighborsArray, PyArrayObject *__pyx_v_elementMaterialTypes, PyArrayObject *__pyx_v_q_flin, PyArrayObject *__pyx_v_q_alin); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_30RE_NCP1_evaluateElementCoefficients_VGM(CYTHON_UNUSED PyObject *__pyx_self, double __pyx_v_rho, double __pyx_v_beta, PyArrayObject *__pyx_v_gravity, PyArrayObject *__pyx_v_alpha, PyArrayObject *__pyx_v_n, PyArrayObject *__pyx_v_thetaR, PyArrayObject *__pyx_v_thetaSR, int __pyx_v_nSpace, int __pyx_v_nElements_global, int __pyx_v_nElementBoundaries_element, PyArrayObject *__pyx_v_elementNeighborsArray, PyArrayObject *__pyx_v_elementBarycentersArray, PyArrayObject *__pyx_v_elementMaterialTypes, int __pyx_v_nDOF_trial_element, PyArrayObject *__pyx_v_u_l2g, PyArrayObject *__pyx_v_u_dof, CYTHON_UNUSED PyArrayObject *__pyx_v_q_x, PyArrayObject *__pyx_v_q_u, PyArrayObject *__pyx_v_q_mass, PyArrayObject *__pyx_v_q_dmass, PyArrayObject *__pyx_v_q_r, PyArrayObject *__pyx_v_q_kr, PyArrayObject *__pyx_v_q_dkr, PyArrayObject *__pyx_v_q_kr_up); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_32RE_NCP1_getElementResidual(CYTHON_UNUSED PyObject *__pyx_self, CYTHON_UNUSED PyArrayObject *__pyx_v_gravity, PyArrayObject *__pyx_v_rowptr, PyArrayObject *__pyx_v_colind, int __pyx_v_nSpace, int __pyx_v_nElements_global, int __pyx_v_nElementBoundaries_element, CYTHON_UNUSED PyArrayObject *__pyx_v_elementNeighborsArray, CYTHON_UNUSED PyArrayObject *__pyx_v_elementBarycentersArray, int __pyx_v_nDOF_test_element, PyArrayObject *__pyx_v_q_u, PyArrayObject *__pyx_v_q_grad_u, PyArrayObject *__pyx_v_q_grad_w, PyArrayObject *__pyx_v_q_detJ, PyArrayObject *__pyx_v_q_m, PyArrayObject *__pyx_v_q_mt, PyArrayObject *__pyx_v_q_r, PyArrayObject *__pyx_v_q_kr, PyArrayObject *__pyx_v_q_kr_up, PyArrayObject *__pyx_v_q_flin, PyArrayObject *__pyx_v_q_alin, PyArrayObject *__pyx_v_elementResidual); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_34RE_NCP1_getElementJacobian(CYTHON_UNUSED PyObject *__pyx_self, CYTHON_UNUSED PyArrayObject *__pyx_v_gravity, PyArrayObject *__pyx_v_rowptr, PyArrayObject *__pyx_v_colind, int __pyx_v_nSpace, int __pyx_v_nElements_global, int __pyx_v_nElementBoundaries_element, CYTHON_UNUSED PyArrayObject *__pyx_v_elementNeighborsArray, CYTHON_UNUSED PyArrayObject *__pyx_v_elementBarycentersArray, int __pyx_v_nDOF_test_element, int __pyx_v_nDOF_trial_element, PyArrayObject *__pyx_v_q_u, CYTHON_UNUSED PyArrayObject *__pyx_v_q_grad_u, PyArrayObject *__pyx_v_q_grad_w, PyArrayObject *__pyx_v_q_grad_v, PyArrayObject *__pyx_v_q_detJ, PyArrayObject *__pyx_v_q_m, CYTHON_UNUSED PyArrayObject *__pyx_v_q_dm, PyArrayObject *__pyx_v_q_mt, PyArrayObject *__pyx_v_q_dmt, PyArrayObject *__pyx_v_q_r, PyArrayObject *__pyx_v_q_kr, CYTHON_UNUSED PyArrayObject *__pyx_v_q_dkr, PyArrayObject *__pyx_v_q_kr_up, PyArrayObject *__pyx_v_q_flin, PyArrayObject *__pyx_v_q_alin, PyArrayObject *__pyx_v_elementJacobian); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_36updateMass_weakAvg(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_mt, PyArrayObject *__pyx_v_w, PyArrayObject *__pyx_v_dV, PyArrayObject *__pyx_v_weak_residual); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_38updateMassJacobian_weakAvg(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_dmt, PyArrayObject *__pyx_v_w, PyArrayObject *__pyx_v_v, PyArrayObject *__pyx_v_dV, PyArrayObject *__pyx_v_jacobian_weak_residual); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_40calculateNormalFlux(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_v, PyArrayObject *__pyx_v_n, PyArrayObject *__pyx_v_dS, PyArrayObject *__pyx_v_flux); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_42computeSimpleCharacteristicVelocityFromElementVelocity(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_df, PyArrayObject *__pyx_v_characteristic_velocity, PyArrayObject *__pyx_v_dm, PyArrayObject *__pyx_v_dV); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_44computeSimpleCharacteristicVelocityFromVelocityDOFs(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_df_dofs, PyArrayObject *__pyx_v_characteristic_velocity_dofs, PyArrayObject *__pyx_v_l2g, PyArrayObject *__pyx_v_dm, PyArrayObject *__pyx_v_dV); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_46rotatingGaussianElementVelocityEval3(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_transient, double __pyx_v_t, double __pyx_v_tForReversal, double __pyx_v_clock, double __pyx_v_xc, double __pyx_v_yc, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_v, double __pyx_v_zvelocity); /* proto */

static PyObject *__pyx_pf_28subsurfaceTransportFunctions_48rotatingGaussianElementVelocityEval4(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_transient, double __pyx_v_t, double __pyx_v_tForReversal, double __pyx_v_clock, double __pyx_v_xc, double __pyx_v_yc, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_v, double __pyx_v_zvelocity); /* proto */

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static PyObject *__pyx_pf_28subsurfaceTransportFunctions_52helicalElementVelocityEval4(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_transient, double __pyx_v_t, double __pyx_v_tForReversal, double __pyx_v_clock, double __pyx_v_zVelocity, double __pyx_v_xc, double __pyx_v_yc, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_v); /* proto */

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/* "subsurfaceTransportFunctions.pyx":359

 *

 *

 * def RE_NCP1_evaluateElementCoefficients_VGM(double rho,             # <<<<<<<<<<<<<<

 *                                             double beta,

 *                                             numpy.ndarray[DTYPE_t,ndim=1] gravity,#physical quantities

 */


/* Python wrapper */

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static char __pyx_doc_28subsurfaceTransportFunctions_30RE_NCP1_evaluateElementCoefficients_VGM[] = "\n    routine for evaluating nodal coefficients in NCP1 approximation for conservative head formulation of Richards equation \n\n    Approximation:\n         uses  nodal quadrature where the nodes are face barycenters\n         uses harmonic average for intrinsic permeability/ hydraulic conductivity\n         assumes slight compressiblity for now\n\n    TODO:\n         everything\n         \n    ";

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 */

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 *

 */

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 *

 *                 sBar = pow(onePlus_pcBar_n,-m)

 */

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 *

 *                 sBar = pow(onePlus_pcBar_n,-m)             # <<<<<<<<<<<<<<

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 */

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 *

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 *

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 */

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 *

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 *

 */

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 *

 *                 thetaW = thetaSR[matID]*sBar + thetaR[matID]

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 *

 *                 thetaW = thetaSR[matID]*sBar + thetaR[matID]             # <<<<<<<<<<<<<<

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 *

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 *

 *                 thetaW = thetaSR[matID]*sBar + thetaR[matID]

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 *

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 *

 *                 sqrt_sBar = sqrt(sBar)             # <<<<<<<<<<<<<<

 *                 KWr= sqrt_sBar*vBar2

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 */

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 *

 *                 sqrt_sBar = sqrt(sBar)

 *                 KWr= sqrt_sBar*vBar2             # <<<<<<<<<<<<<<

 *                 DKWr_DpsiC= ((0.5/sqrt_sBar)*DsBar_DpsiC*vBar2 + 2.0*sqrt_sBar*vBar*DvBar_DpsiC)

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 */

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 *                 DKWr_DpsiC= ((0.5/sqrt_sBar)*DsBar_DpsiC*vBar2 + 2.0*sqrt_sBar*vBar*DvBar_DpsiC)             # <<<<<<<<<<<<<<

 *             else:

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 *             m = 1.0 - 1.0/n[matID]

 *             thetaS = thetaR[matID] + thetaSR[matID]

 *             if psiC > 0.0:             # <<<<<<<<<<<<<<

 *                 pcBar = alpha[matID]*psiC

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 */

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 */

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 *             else:

 *                 thetaW        = thetaS

 *                 DthetaW_DpsiC = 0.0             # <<<<<<<<<<<<<<

 *                 KWr           = 1.0

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 */

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 *                 thetaW        = thetaS

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 *                 DKWr_DpsiC    = 0.0

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 */

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 *             #

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 */

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 *                 DKWr_DpsiC    = 0.0

 *             #

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 */

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 *             #

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 *             drhom= beta*rhom             # <<<<<<<<<<<<<<

 *             q_mass[eN,j] = rhom*thetaW

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 */

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 *             drhom= beta*rhom

 *             q_mass[eN,j] = rhom*thetaW             # <<<<<<<<<<<<<<

 *             q_dmass[eN,j]=-rhom*DthetaW_DpsiC+drhom*thetaW

 *

 */

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 *

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 *                                                 material_functions[material_right])

 *

 * def setSparseTensorMaterialFunctionOverElementBoundaries_harmonicAverage(int nd,             # <<<<<<<<<<<<<<

 *                                                                          numpy.ndarray[ITYPE_t,ndim=2] elementBoundariesArray,

 *                                                                          numpy.ndarray[ITYPE_t,ndim=2] elementBoundaryTypes,

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 *                         ebq_vals[eN,ebN_local,k,I*nd+J] = numer/denom

 *

 * def setScalarMaterialFunctionOverGlobalElementBoundaries_arithmeticAverage(numpy.ndarray[ITYPE_t,ndim=2] elementBoundariesArray,             # <<<<<<<<<<<<<<

 *                                                                            numpy.ndarray[ITYPE_t,ndim=2] elementBoundaryTypes,

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 *

 *

 * def setSparseTensorMaterialFunctionOverGlobalElementBoundaries_harmonicAverage(int nd,             # <<<<<<<<<<<<<<

 *                                                                                numpy.ndarray[ITYPE_t,ndim=2] elementBoundariesArray,

 *                                                                                numpy.ndarray[ITYPE_t,ndim=2] elementBoundaryTypes,

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 *

 * ###

 * def evaluateScalarMaterialFunctionOverElements(double t,             # <<<<<<<<<<<<<<

 *                                                numpy.ndarray[ITYPE_t,ndim=1] elementMaterialTypes,

 *                                                numpy.ndarray[DTYPE_t,ndim=3] x,

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 *             q_vals[eN,k] = material_functions[material](x[eN,k],t)

 *

 * def evaluateVectorMaterialFunctionOverElements(double t,             # <<<<<<<<<<<<<<

 *                                                numpy.ndarray[ITYPE_t,ndim=1] elementMaterialTypes,

 *                                                numpy.ndarray[DTYPE_t,ndim=3] x,

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 *

 *

 * def evaluateScalarMaterialFunctionOverElementBoundaries_arithmeticAverage(double t,             # <<<<<<<<<<<<<<

 *                                                                           numpy.ndarray[ITYPE_t,ndim=2] elementBoundariesArray,

 *                                                                           numpy.ndarray[ITYPE_t,ndim=2] elementBoundaryTypes,

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 *                                                 material_functions[material_right](x[eN,ebN_local,k],t))

 *

 * def evaluateSparseTensorMaterialFunctionOverElementBoundaries_harmonicAverage(int nd,             # <<<<<<<<<<<<<<

 *                                                                               double t,

 *                                                                               numpy.ndarray[ITYPE_t,ndim=2] elementBoundariesArray,

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 *                         ebq_vals[eN,ebN_local,k,I*nd+J] = numer/denom

 *

 * def evaluateScalarMaterialFunctionOverGlobalElementBoundaries_arithmeticAverage(double t,             # <<<<<<<<<<<<<<

 *                                                                                 numpy.ndarray[ITYPE_t,ndim=2] elementBoundariesArray,

 *                                                                                 numpy.ndarray[ITYPE_t,ndim=2] elementBoundaryTypes,

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 *

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 * def evaluateSparseTensorMaterialFunctionOverGlobalElementBoundaries_harmonicAverage(int nd,             # <<<<<<<<<<<<<<

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 *

 * ##################################################

 * def RE_NCP1_evaluateElementCoefficients_Linear(double rho,             # <<<<<<<<<<<<<<

 *                                                numpy.ndarray[DTYPE_t,ndim=1] gravity,#physical quantities

 *                                                numpy.ndarray[ITYPE_t,ndim=1] rowptr,

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 *

 *

 * def RE_NCP1_evaluateElementCoefficients_VGM(double rho,             # <<<<<<<<<<<<<<

 *                                             double beta,

 *                                             numpy.ndarray[DTYPE_t,ndim=1] gravity,#physical quantities

 */

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  /* "subsurfaceTransportFunctions.pyx":486

 *     #eN for upwind

 *

 * def RE_NCP1_getElementResidual(numpy.ndarray[DTYPE_t,ndim=1] gravity,#physical quantities             # <<<<<<<<<<<<<<

 *                                numpy.ndarray[ITYPE_t,ndim=1] rowptr,

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  /* "subsurfaceTransportFunctions.pyx":574

 *         #i

 *     #eN

 * def RE_NCP1_getElementJacobian(numpy.ndarray[DTYPE_t,ndim=1] gravity,#physical quantities             # <<<<<<<<<<<<<<

 *                                numpy.ndarray[ITYPE_t,ndim=1] rowptr,

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  ctx->enc_type = 0;

  ctx->is_complex = 0;

  ctx->is_valid_array = 0;

  ctx->struct_alignment = 0;

  while (type->typegroup == 'S') {

    ++ctx->head;

    ctx->head->field = type->fields;

    ctx->head->parent_offset = 0;

    type = type->fields->type;

  }

}

static int __Pyx_BufFmt_ParseNumber(const char** ts) {

    int count;

    const char* t = *ts;

    if (*t < '0' || *t > '9') {

      return -1;

    } else {

        count = *t++ - '0';

        while (*t >= '0' && *t <= '9') {

            count *= 10;

            count += *t++ - '0';

        }

    }

    *ts = t;

    return count;

}

static int __Pyx_BufFmt_ExpectNumber(const char **ts) {

    int number = __Pyx_BufFmt_ParseNumber(ts);

    if (number == -1)

        PyErr_Format(PyExc_ValueError,\

                     "Does not understand character buffer dtype format string ('%c')", **ts);

    return number;

}

static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {

  PyErr_Format(PyExc_ValueError,

               "Unexpected format string character: '%c'", ch);

}

static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {

  switch (ch) {

    case '?': return "'bool'";

    case 'c': return "'char'";

    case 'b': return "'signed char'";

    case 'B': return "'unsigned char'";

    case 'h': return "'short'";

    case 'H': return "'unsigned short'";

    case 'i': return "'int'";

    case 'I': return "'unsigned int'";

    case 'l': return "'long'";

    case 'L': return "'unsigned long'";

    case 'q': return "'long long'";

    case 'Q': return "'unsigned long long'";

    case 'f': return (is_complex ? "'complex float'" : "'float'");

    case 'd': return (is_complex ? "'complex double'" : "'double'");

    case 'g': return (is_complex ? "'complex long double'" : "'long double'");

    case 'T': return "a struct";

    case 'O': return "Python object";

    case 'P': return "a pointer";

    case 's': case 'p': return "a string";

    case 0: return "end";

    default: return "unparseable format string";

  }

}

static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {

  switch (ch) {

    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;

    case 'h': case 'H': return 2;

    case 'i': case 'I': case 'l': case 'L': return 4;

    case 'q': case 'Q': return 8;

    case 'f': return (is_complex ? 8 : 4);

    case 'd': return (is_complex ? 16 : 8);

    case 'g': {

      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");

      return 0;

    }

    case 'O': case 'P': return sizeof(void*);

    default:

      __Pyx_BufFmt_RaiseUnexpectedChar(ch);

      return 0;

    }

}

static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {

  switch (ch) {

    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;

    case 'h': case 'H': return sizeof(short);

    case 'i': case 'I': return sizeof(int);

    case 'l': case 'L': return sizeof(long);

    #ifdef HAVE_LONG_LONG

    case 'q': case 'Q': return sizeof(PY_LONG_LONG);

    #endif

    case 'f': return sizeof(float) * (is_complex ? 2 : 1);

    case 'd': return sizeof(double) * (is_complex ? 2 : 1);

    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);

    case 'O': case 'P': return sizeof(void*);

    default: {

      __Pyx_BufFmt_RaiseUnexpectedChar(ch);

      return 0;

    }

  }

}

typedef struct { char c; short x; } __Pyx_st_short;

typedef struct { char c; int x; } __Pyx_st_int;

typedef struct { char c; long x; } __Pyx_st_long;

typedef struct { char c; float x; } __Pyx_st_float;

typedef struct { char c; double x; } __Pyx_st_double;

typedef struct { char c; long double x; } __Pyx_st_longdouble;

typedef struct { char c; void *x; } __Pyx_st_void_p;

#ifdef HAVE_LONG_LONG

typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;

#endif

static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {

  switch (ch) {

    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;

    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);

    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);

    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);

#ifdef HAVE_LONG_LONG

    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);

#endif

    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);

    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);

    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);

    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);

    default:

      __Pyx_BufFmt_RaiseUnexpectedChar(ch);

      return 0;

    }

}

/* These are for computing the padding at the end of the struct to align

   on the first member of the struct. This will probably the same as above,

   but we don't have any guarantees.

 */

typedef struct { short x; char c; } __Pyx_pad_short;

typedef struct { int x; char c; } __Pyx_pad_int;

typedef struct { long x; char c; } __Pyx_pad_long;

typedef struct { float x; char c; } __Pyx_pad_float;

typedef struct { double x; char c; } __Pyx_pad_double;

typedef struct { long double x; char c; } __Pyx_pad_longdouble;

typedef struct { void *x; char c; } __Pyx_pad_void_p;

#ifdef HAVE_LONG_LONG

typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;

#endif

static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {

  switch (ch) {

    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;

    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);

    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);

    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);

#ifdef HAVE_LONG_LONG

    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);

#endif

    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);

    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);

    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);

    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);

    default:

      __Pyx_BufFmt_RaiseUnexpectedChar(ch);

      return 0;

    }

}

static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {

  switch (ch) {

    case 'c':

        return 'H';

    case 'b': case 'h': case 'i':

    case 'l': case 'q': case 's': case 'p':

        return 'I';

    case '?': case 'B': case 'H': case 'I': case 'L': case 'Q':

        return 'U';

    case 'f': case 'd': case 'g':

        return (is_complex ? 'C' : 'R');

    case 'O':

        return 'O';

    case 'P':

        return 'P';

    default: {

      __Pyx_BufFmt_RaiseUnexpectedChar(ch);

      return 0;

    }

  }

}

static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {

  if (ctx->head == NULL || ctx->head->field == &ctx->root) {

    const char* expected;

    const char* quote;

    if (ctx->head == NULL) {

      expected = "end";

      quote = "";

    } else {

      expected = ctx->head->field->type->name;

      quote = "'";

    }

    PyErr_Format(PyExc_ValueError,

                 "Buffer dtype mismatch, expected %s%s%s but got %s",

                 quote, expected, quote,

                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));

  } else {

    __Pyx_StructField* field = ctx->head->field;

    __Pyx_StructField* parent = (ctx->head - 1)->field;

    PyErr_Format(PyExc_ValueError,

                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",

                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),

                 parent->type->name, field->name);

  }

}

static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {

  char group;

  size_t size, offset, arraysize = 1;

  if (ctx->enc_type == 0) return 0;

  if (ctx->head->field->type->arraysize[0]) {

    int i, ndim = 0;

    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {

        ctx->is_valid_array = ctx->head->field->type->ndim == 1;

        ndim = 1;

        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {

            PyErr_Format(PyExc_ValueError,

                         "Expected a dimension of size %zu, got %zu",

                         ctx->head->field->type->arraysize[0], ctx->enc_count);

            return -1;

        }

    }

    if (!ctx->is_valid_array) {

      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",

                   ctx->head->field->type->ndim, ndim);

      return -1;

    }

    for (i = 0; i < ctx->head->field->type->ndim; i++) {

      arraysize *= ctx->head->field->type->arraysize[i];

    }

    ctx->is_valid_array = 0;

    ctx->enc_count = 1;

  }

  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);

  do {

    __Pyx_StructField* field = ctx->head->field;

    __Pyx_TypeInfo* type = field->type;

    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {

      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);

    } else {

      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);

    }

    if (ctx->enc_packmode == '@') {

      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);

      size_t align_mod_offset;

      if (align_at == 0) return -1;

      align_mod_offset = ctx->fmt_offset % align_at;

      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;

      if (ctx->struct_alignment == 0)

          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,

                                                                 ctx->is_complex);

    }

    if (type->size != size || type->typegroup != group) {

      if (type->typegroup == 'C' && type->fields != NULL) {

        size_t parent_offset = ctx->head->parent_offset + field->offset;

        ++ctx->head;

        ctx->head->field = type->fields;

        ctx->head->parent_offset = parent_offset;

        continue;

      }

      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {

      } else {

          __Pyx_BufFmt_RaiseExpected(ctx);

          return -1;

      }

    }

    offset = ctx->head->parent_offset + field->offset;

    if (ctx->fmt_offset != offset) {

      PyErr_Format(PyExc_ValueError,

                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",

                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);

      return -1;

    }

    ctx->fmt_offset += size;

    if (arraysize)

      ctx->fmt_offset += (arraysize - 1) * size;

    --ctx->enc_count;

    while (1) {

      if (field == &ctx->root) {

        ctx->head = NULL;

        if (ctx->enc_count != 0) {

          __Pyx_BufFmt_RaiseExpected(ctx);

          return -1;

        }

        break;

      }

      ctx->head->field = ++field;

      if (field->type == NULL) {

        --ctx->head;

        field = ctx->head->field;

        continue;

      } else if (field->type->typegroup == 'S') {

        size_t parent_offset = ctx->head->parent_offset + field->offset;

        if (field->type->fields->type == NULL) continue;

        field = field->type->fields;

        ++ctx->head;

        ctx->head->field = field;

        ctx->head->parent_offset = parent_offset;

        break;

      } else {

        break;

      }

    }

  } while (ctx->enc_count);

  ctx->enc_type = 0;

  ctx->is_complex = 0;

  return 0;

}

static PyObject *

__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)

{

    const char *ts = *tsp;

    int i = 0, number, ndim;

    ++ts;

    if (ctx->new_count != 1) {

        PyErr_SetString(PyExc_ValueError,

                        "Cannot handle repeated arrays in format string");

        return NULL;

    }

    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;

    ndim = ctx->head->field->type->ndim;

    while (*ts && *ts != ')') {

        switch (*ts) {

            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;

            default:  break;

        }

        number = __Pyx_BufFmt_ExpectNumber(&ts);

        if (number == -1) return NULL;

        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])

            return PyErr_Format(PyExc_ValueError,

                        "Expected a dimension of size %zu, got %d",

                        ctx->head->field->type->arraysize[i], number);

        if (*ts != ',' && *ts != ')')

            return PyErr_Format(PyExc_ValueError,

                                "Expected a comma in format string, got '%c'", *ts);

        if (*ts == ',') ts++;

        i++;

    }

    if (i != ndim)

        return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",

                            ctx->head->field->type->ndim, i);

    if (!*ts) {

        PyErr_SetString(PyExc_ValueError,

                        "Unexpected end of format string, expected ')'");

        return NULL;

    }

    ctx->is_valid_array = 1;

    ctx->new_count = 1;

    *tsp = ++ts;

    return Py_None;

}

static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {

  int got_Z = 0;

  while (1) {

    switch(*ts) {

      case 0:

        if (ctx->enc_type != 0 && ctx->head == NULL) {

          __Pyx_BufFmt_RaiseExpected(ctx);

          return NULL;

        }

        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;

        if (ctx->head != NULL) {

          __Pyx_BufFmt_RaiseExpected(ctx);

          return NULL;

        }

        return ts;

      case ' ':

      case '\r':

      case '\n':

        ++ts;

        break;

      case '<':

        if (!__Pyx_Is_Little_Endian()) {

          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");

          return NULL;

        }

        ctx->new_packmode = '=';

        ++ts;

        break;

      case '>':

      case '!':

        if (__Pyx_Is_Little_Endian()) {

          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");

          return NULL;

        }

        ctx->new_packmode = '=';

        ++ts;

        break;

      case '=':

      case '@':

      case '^':

        ctx->new_packmode = *ts++;

        break;

      case 'T':

        {

          const char* ts_after_sub;

          size_t i, struct_count = ctx->new_count;

          size_t struct_alignment = ctx->struct_alignment;

          ctx->new_count = 1;

          ++ts;

          if (*ts != '{') {

            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");

            return NULL;

          }

          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;

          ctx->enc_type = 0;

          ctx->enc_count = 0;

          ctx->struct_alignment = 0;

          ++ts;

          ts_after_sub = ts;

          for (i = 0; i != struct_count; ++i) {

            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);

            if (!ts_after_sub) return NULL;

          }

          ts = ts_after_sub;

          if (struct_alignment) ctx->struct_alignment = struct_alignment;

        }

        break;

      case '}':

        {

          size_t alignment = ctx->struct_alignment;

          ++ts;

          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;

          ctx->enc_type = 0;

          if (alignment && ctx->fmt_offset % alignment) {

            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);

          }

        }

        return ts;

      case 'x':

        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;

        ctx->fmt_offset += ctx->new_count;

        ctx->new_count = 1;

        ctx->enc_count = 0;

        ctx->enc_type = 0;

        ctx->enc_packmode = ctx->new_packmode;

        ++ts;

        break;

      case 'Z':

        got_Z = 1;

        ++ts;

        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {

          __Pyx_BufFmt_RaiseUnexpectedChar('Z');

          return NULL;

        }

        CYTHON_FALLTHROUGH;

      case '?': case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':

      case 'l': case 'L': case 'q': case 'Q':

      case 'f': case 'd': case 'g':

      case 'O': case 'p':

        if ((ctx->enc_type == *ts) && (got_Z == ctx->is_complex) &&

            (ctx->enc_packmode == ctx->new_packmode) && (!ctx->is_valid_array)) {

          ctx->enc_count += ctx->new_count;

          ctx->new_count = 1;

          got_Z = 0;

          ++ts;

          break;

        }

        CYTHON_FALLTHROUGH;

      case 's':

        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;

        ctx->enc_count = ctx->new_count;

        ctx->enc_packmode = ctx->new_packmode;

        ctx->enc_type = *ts;

        ctx->is_complex = got_Z;

        ++ts;

        ctx->new_count = 1;

        got_Z = 0;

        break;

      case ':':

        ++ts;

        while(*ts != ':') ++ts;

        ++ts;

        break;

      case '(':

        if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;

        break;

      default:

        {

          int number = __Pyx_BufFmt_ExpectNumber(&ts);

          if (number == -1) return NULL;

          ctx->new_count = (size_t)number;

        }

    }

  }

}


/* BufferGetAndValidate */

  static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {

  if (unlikely(info->buf == NULL)) return;

  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;

  __Pyx_ReleaseBuffer(info);

}

static void __Pyx_ZeroBuffer(Py_buffer* buf) {

  buf->buf = NULL;

  buf->obj = NULL;

  buf->strides = __Pyx_zeros;

  buf->shape = __Pyx_zeros;

  buf->suboffsets = __Pyx_minusones;

}

static int __Pyx__GetBufferAndValidate(

        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,

        int nd, int cast, __Pyx_BufFmt_StackElem* stack)

{

  buf->buf = NULL;

  if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) {

    __Pyx_ZeroBuffer(buf);

    return -1;

  }

  if (unlikely(buf->ndim != nd)) {

    PyErr_Format(PyExc_ValueError,

                 "Buffer has wrong number of dimensions (expected %d, got %d)",

                 nd, buf->ndim);

    goto fail;

  }

  if (!cast) {

    __Pyx_BufFmt_Context ctx;

    __Pyx_BufFmt_Init(&ctx, stack, dtype);

    if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;

  }

  if (unlikely((size_t)buf->itemsize != dtype->size)) {

    PyErr_Format(PyExc_ValueError,

      "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",

      buf->itemsize, (buf->itemsize > 1) ? "s" : "",

      dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");

    goto fail;

  }

  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;

  return 0;

fail:;

  __Pyx_SafeReleaseBuffer(buf);

  return -1;

}


/* BufferIndexError */

  static void __Pyx_RaiseBufferIndexError(int axis) {

  PyErr_Format(PyExc_IndexError,

     "Out of bounds on buffer access (axis %d)", axis);

}


/* PyErrFetchRestore */

  #if CYTHON_FAST_THREAD_STATE

static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {

    PyObject *tmp_type, *tmp_value, *tmp_tb;

    tmp_type = tstate->curexc_type;

    tmp_value = tstate->curexc_value;

    tmp_tb = tstate->curexc_traceback;

    tstate->curexc_type = type;

    tstate->curexc_value = value;

    tstate->curexc_traceback = tb;

    Py_XDECREF(tmp_type);

    Py_XDECREF(tmp_value);

    Py_XDECREF(tmp_tb);

}

static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {

    *type = tstate->curexc_type;

    *value = tstate->curexc_value;

    *tb = tstate->curexc_traceback;

    tstate->curexc_type = 0;

    tstate->curexc_value = 0;

    tstate->curexc_traceback = 0;

}

#endif


/* DictGetItem */

  #if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY

static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) {

    PyObject *value;

    value = PyDict_GetItemWithError(d, key);

    if (unlikely(!value)) {

        if (!PyErr_Occurred()) {

            if (unlikely(PyTuple_Check(key))) {

                PyObject* args = PyTuple_Pack(1, key);

                if (likely(args)) {

                    PyErr_SetObject(PyExc_KeyError, args);

                    Py_DECREF(args);

                }

            } else {

                PyErr_SetObject(PyExc_KeyError, key);

            }

        }

        return NULL;

    }

    Py_INCREF(value);

    return value;

}

#endif


/* GetItemInt */

  static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {

    PyObject *r;

    if (!j) return NULL;

    r = PyObject_GetItem(o, j);

    Py_DECREF(j);

    return r;

}

static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,

                                                              CYTHON_NCP_UNUSED int wraparound,

                                                              CYTHON_NCP_UNUSED int boundscheck) {

#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS

    Py_ssize_t wrapped_i = i;

    if (wraparound & unlikely(i < 0)) {

        wrapped_i += PyList_GET_SIZE(o);

    }

    if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyList_GET_SIZE(o)))) {

        PyObject *r = PyList_GET_ITEM(o, wrapped_i);

        Py_INCREF(r);

        return r;

    }

    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));

#else

    return PySequence_GetItem(o, i);

#endif

}

static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,

                                                              CYTHON_NCP_UNUSED int wraparound,

                                                              CYTHON_NCP_UNUSED int boundscheck) {

#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS

    Py_ssize_t wrapped_i = i;

    if (wraparound & unlikely(i < 0)) {

        wrapped_i += PyTuple_GET_SIZE(o);

    }

    if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyTuple_GET_SIZE(o)))) {

        PyObject *r = PyTuple_GET_ITEM(o, wrapped_i);

        Py_INCREF(r);

        return r;

    }

    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));

#else

    return PySequence_GetItem(o, i);

#endif

}

static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list,

                                                     CYTHON_NCP_UNUSED int wraparound,

                                                     CYTHON_NCP_UNUSED int boundscheck) {

#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS

    if (is_list || PyList_CheckExact(o)) {

        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);

        if ((!boundscheck) || (likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o))))) {

            PyObject *r = PyList_GET_ITEM(o, n);

            Py_INCREF(r);

            return r;

        }

    }

    else if (PyTuple_CheckExact(o)) {

        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);

        if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyTuple_GET_SIZE(o)))) {

            PyObject *r = PyTuple_GET_ITEM(o, n);

            Py_INCREF(r);

            return r;

        }

    } else {

        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;

        if (likely(m && m->sq_item)) {

            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {

                Py_ssize_t l = m->sq_length(o);

                if (likely(l >= 0)) {

                    i += l;

                } else {

                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))

                        return NULL;

                    PyErr_Clear();

                }

            }

            return m->sq_item(o, i);

        }

    }

#else

    if (is_list || PySequence_Check(o)) {

        return PySequence_GetItem(o, i);

    }

#endif

    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));

}


/* ObjectGetItem */

  #if CYTHON_USE_TYPE_SLOTS

static PyObject *__Pyx_PyObject_GetIndex(PyObject *obj, PyObject* index) {

    PyObject *runerr;

    Py_ssize_t key_value;

    PySequenceMethods *m = Py_TYPE(obj)->tp_as_sequence;

    if (unlikely(!(m && m->sq_item))) {

        PyErr_Format(PyExc_TypeError, "'%.200s' object is not subscriptable", Py_TYPE(obj)->tp_name);

        return NULL;

    }

    key_value = __Pyx_PyIndex_AsSsize_t(index);

    if (likely(key_value != -1 || !(runerr = PyErr_Occurred()))) {

        return __Pyx_GetItemInt_Fast(obj, key_value, 0, 1, 1);

    }

    if (PyErr_GivenExceptionMatches(runerr, PyExc_OverflowError)) {

        PyErr_Clear();

        PyErr_Format(PyExc_IndexError, "cannot fit '%.200s' into an index-sized integer", Py_TYPE(index)->tp_name);

    }

    return NULL;

}

static PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject* key) {

    PyMappingMethods *m = Py_TYPE(obj)->tp_as_mapping;

    if (likely(m && m->mp_subscript)) {

        return m->mp_subscript(obj, key);

    }

    return __Pyx_PyObject_GetIndex(obj, key);

}

#endif


/* PyFloatBinop */

  #if !CYTHON_COMPILING_IN_PYPY

static PyObject* __Pyx_PyFloat_AddObjC(PyObject *op1, PyObject *op2, double floatval, int inplace, int zerodivision_check) {

    const double b = floatval;

    double a, result;

    (void)inplace;

    (void)zerodivision_check;

    if (likely(PyFloat_CheckExact(op1))) {

        a = PyFloat_AS_DOUBLE(op1);


    } else

    #if PY_MAJOR_VERSION < 3

    if (likely(PyInt_CheckExact(op1))) {

        a = (double) PyInt_AS_LONG(op1);


    } else

    #endif

    if (likely(PyLong_CheckExact(op1))) {

        #if CYTHON_USE_PYLONG_INTERNALS

        const digit* digits = ((PyLongObject*)op1)->ob_digit;

        const Py_ssize_t size = Py_SIZE(op1);

        switch (size) {

            case  0: a = 0.0; break;

            case -1: a = -(double) digits[0]; break;

            case  1: a = (double) digits[0]; break;

            case -2:

            case 2:

                if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) {

                    a = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));

                    if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {

                        if (size == -2)

                            a = -a;

                        break;

                    }

                }

                CYTHON_FALLTHROUGH;

            case -3:

            case 3:

                if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) {

                    a = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));

                    if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {

                        if (size == -3)

                            a = -a;

                        break;

                    }

                }

                CYTHON_FALLTHROUGH;

            case -4:

            case 4:

                if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) {

                    a = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));

                    if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) {

                        if (size == -4)

                            a = -a;

                        break;

                    }

                }

                CYTHON_FALLTHROUGH;

            default:

        #else

        {

        #endif

            a = PyLong_AsDouble(op1);

            if (unlikely(a == -1.0 && PyErr_Occurred())) return NULL;


        }

    } else {

        return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);

    }


        PyFPE_START_PROTECT("add", return NULL)

        result = a + b;

        PyFPE_END_PROTECT(result)

        return PyFloat_FromDouble(result);

}

#endif


/* PyFunctionFastCall */

    #if CYTHON_FAST_PYCALL

static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,

                                               PyObject *globals) {

    PyFrameObject *f;

    PyThreadState *tstate = __Pyx_PyThreadState_Current;

    PyObject **fastlocals;

    Py_ssize_t i;

    PyObject *result;

    assert(globals != NULL);

    /* XXX Perhaps we should create a specialized

       PyFrame_New() that doesn't take locals, but does

       take builtins without sanity checking them.

       */

    assert(tstate != NULL);

    f = PyFrame_New(tstate, co, globals, NULL);

    if (f == NULL) {

        return NULL;

    }

    fastlocals = __Pyx_PyFrame_GetLocalsplus(f);

    for (i = 0; i < na; i++) {

        Py_INCREF(*args);

        fastlocals[i] = *args++;

    }

    result = PyEval_EvalFrameEx(f,0);

    ++tstate->recursion_depth;

    Py_DECREF(f);

    --tstate->recursion_depth;

    return result;

}

#if 1 || PY_VERSION_HEX < 0x030600B1

static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs) {

    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);

    PyObject *globals = PyFunction_GET_GLOBALS(func);

    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);

    PyObject *closure;

#if PY_MAJOR_VERSION >= 3

    PyObject *kwdefs;

#endif

    PyObject *kwtuple, **k;

    PyObject **d;

    Py_ssize_t nd;

    Py_ssize_t nk;

    PyObject *result;

    assert(kwargs == NULL || PyDict_Check(kwargs));

    nk = kwargs ? PyDict_Size(kwargs) : 0;

    if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {

        return NULL;

    }

    if (

#if PY_MAJOR_VERSION >= 3

            co->co_kwonlyargcount == 0 &&

#endif

            likely(kwargs == NULL || nk == 0) &&

            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {

        if (argdefs == NULL && co->co_argcount == nargs) {

            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);

            goto done;

        }

        else if (nargs == 0 && argdefs != NULL

                 && co->co_argcount == Py_SIZE(argdefs)) {

            /* function called with no arguments, but all parameters have

               a default value: use default values as arguments .*/

            args = &PyTuple_GET_ITEM(argdefs, 0);

            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);

            goto done;

        }

    }

    if (kwargs != NULL) {

        Py_ssize_t pos, i;

        kwtuple = PyTuple_New(2 * nk);

        if (kwtuple == NULL) {

            result = NULL;

            goto done;

        }

        k = &PyTuple_GET_ITEM(kwtuple, 0);

        pos = i = 0;

        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {

            Py_INCREF(k[i]);

            Py_INCREF(k[i+1]);

            i += 2;

        }

        nk = i / 2;

    }

    else {

        kwtuple = NULL;

        k = NULL;

    }

    closure = PyFunction_GET_CLOSURE(func);

#if PY_MAJOR_VERSION >= 3

    kwdefs = PyFunction_GET_KW_DEFAULTS(func);

#endif

    if (argdefs != NULL) {

        d = &PyTuple_GET_ITEM(argdefs, 0);

        nd = Py_SIZE(argdefs);

    }

    else {

        d = NULL;

        nd = 0;

    }

#if PY_MAJOR_VERSION >= 3

    result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,

                               args, (int)nargs,

                               k, (int)nk,

                               d, (int)nd, kwdefs, closure);

#else

    result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,

                               args, (int)nargs,

                               k, (int)nk,

                               d, (int)nd, closure);

#endif

    Py_XDECREF(kwtuple);

done:

    Py_LeaveRecursiveCall();

    return result;

}

#endif

#endif


/* PyCFunctionFastCall */

    #if CYTHON_FAST_PYCCALL

static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {

    PyCFunctionObject *func = (PyCFunctionObject*)func_obj;

    PyCFunction meth = PyCFunction_GET_FUNCTION(func);

    PyObject *self = PyCFunction_GET_SELF(func);

    int flags = PyCFunction_GET_FLAGS(func);

    assert(PyCFunction_Check(func));

    assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)));

    assert(nargs >= 0);

    assert(nargs == 0 || args != NULL);

    /* _PyCFunction_FastCallDict() must not be called with an exception set,

       because it may clear it (directly or indirectly) and so the

       caller loses its exception */

    assert(!PyErr_Occurred());

    if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {

        return (*((__Pyx_PyCFunctionFastWithKeywords)(void*)meth)) (self, args, nargs, NULL);

    } else {

        return (*((__Pyx_PyCFunctionFast)(void*)meth)) (self, args, nargs);

    }

}

#endif


/* PyObjectCall */

    #if CYTHON_COMPILING_IN_CPYTHON

static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {

    PyObject *result;

    ternaryfunc call = func->ob_type->tp_call;

    if (unlikely(!call))

        return PyObject_Call(func, arg, kw);

    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))

        return NULL;

    result = (*call)(func, arg, kw);

    Py_LeaveRecursiveCall();

    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {

        PyErr_SetString(

            PyExc_SystemError,

            "NULL result without error in PyObject_Call");

    }

    return result;

}

#endif


/* PyDictVersioning */

    #if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS

static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) {

    PyObject *dict = Py_TYPE(obj)->tp_dict;

    return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0;

}

static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) {

    PyObject **dictptr = NULL;

    Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;

    if (offset) {

#if CYTHON_COMPILING_IN_CPYTHON

        dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);

#else

        dictptr = _PyObject_GetDictPtr(obj);

#endif

    }

    return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;

}

static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {

    PyObject *dict = Py_TYPE(obj)->tp_dict;

    if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))

        return 0;

    return obj_dict_version == __Pyx_get_object_dict_version(obj);

}

#endif


/* GetModuleGlobalName */

    #if CYTHON_USE_DICT_VERSIONS

static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value)

#else

static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name)

#endif

{

    PyObject *result;

#if !CYTHON_AVOID_BORROWED_REFS

#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1

    result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash);

    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)

    if (likely(result)) {

        return __Pyx_NewRef(result);

    } else if (unlikely(PyErr_Occurred())) {

        return NULL;

    }

#else

    result = PyDict_GetItem(__pyx_d, name);

    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)

    if (likely(result)) {

        return __Pyx_NewRef(result);

    }

#endif

#else

    result = PyObject_GetItem(__pyx_d, name);

    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)

    if (likely(result)) {

        return __Pyx_NewRef(result);

    }

    PyErr_Clear();

#endif

    return __Pyx_GetBuiltinName(name);

}


/* ExtTypeTest */

    static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {

    if (unlikely(!type)) {

        PyErr_SetString(PyExc_SystemError, "Missing type object");

        return 0;

    }

    if (likely(__Pyx_TypeCheck(obj, type)))

        return 1;

    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",

                 Py_TYPE(obj)->tp_name, type->tp_name);

    return 0;

}


/* PyObjectCall2Args */

    static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2) {

    PyObject *args, *result = NULL;

    #if CYTHON_FAST_PYCALL

    if (PyFunction_Check(function)) {

        PyObject *args[2] = {arg1, arg2};

        return __Pyx_PyFunction_FastCall(function, args, 2);

    }

    #endif

    #if CYTHON_FAST_PYCCALL

    if (__Pyx_PyFastCFunction_Check(function)) {

        PyObject *args[2] = {arg1, arg2};

        return __Pyx_PyCFunction_FastCall(function, args, 2);

    }

    #endif

    args = PyTuple_New(2);

    if (unlikely(!args)) goto done;

    Py_INCREF(arg1);

    PyTuple_SET_ITEM(args, 0, arg1);

    Py_INCREF(arg2);

    PyTuple_SET_ITEM(args, 1, arg2);

    Py_INCREF(function);

    result = __Pyx_PyObject_Call(function, args, NULL);

    Py_DECREF(args);

    Py_DECREF(function);

done:

    return result;

}


/* PyObjectCallMethO */

    #if CYTHON_COMPILING_IN_CPYTHON

static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {

    PyObject *self, *result;

    PyCFunction cfunc;

    cfunc = PyCFunction_GET_FUNCTION(func);

    self = PyCFunction_GET_SELF(func);

    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))

        return NULL;

    result = cfunc(self, arg);

    Py_LeaveRecursiveCall();

    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {

        PyErr_SetString(

            PyExc_SystemError,

            "NULL result without error in PyObject_Call");

    }

    return result;

}

#endif


/* PyObjectCallOneArg */

    #if CYTHON_COMPILING_IN_CPYTHON

static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {

    PyObject *result;

    PyObject *args = PyTuple_New(1);

    if (unlikely(!args)) return NULL;

    Py_INCREF(arg);

    PyTuple_SET_ITEM(args, 0, arg);

    result = __Pyx_PyObject_Call(func, args, NULL);

    Py_DECREF(args);

    return result;

}

static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {

#if CYTHON_FAST_PYCALL

    if (PyFunction_Check(func)) {

        return __Pyx_PyFunction_FastCall(func, &arg, 1);

    }

#endif

    if (likely(PyCFunction_Check(func))) {

        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {

            return __Pyx_PyObject_CallMethO(func, arg);

#if CYTHON_FAST_PYCCALL

        } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {

            return __Pyx_PyCFunction_FastCall(func, &arg, 1);

#endif

        }

    }

    return __Pyx__PyObject_CallOneArg(func, arg);

}

#else

static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {

    PyObject *result;

    PyObject *args = PyTuple_Pack(1, arg);

    if (unlikely(!args)) return NULL;

    result = __Pyx_PyObject_Call(func, args, NULL);

    Py_DECREF(args);

    return result;

}

#endif


/* pyobject_as_double */

    static double __Pyx__PyObject_AsDouble(PyObject* obj) {

    PyObject* float_value;

#if !CYTHON_USE_TYPE_SLOTS

    float_value = PyNumber_Float(obj);  if ((0)) goto bad;

#else

    PyNumberMethods *nb = Py_TYPE(obj)->tp_as_number;

    if (likely(nb) && likely(nb->nb_float)) {

        float_value = nb->nb_float(obj);

        if (likely(float_value) && unlikely(!PyFloat_Check(float_value))) {

            PyErr_Format(PyExc_TypeError,

                "__float__ returned non-float (type %.200s)",

                Py_TYPE(float_value)->tp_name);

            Py_DECREF(float_value);

            goto bad;

        }

    } else if (PyUnicode_CheckExact(obj) || PyBytes_CheckExact(obj)) {

#if PY_MAJOR_VERSION >= 3

        float_value = PyFloat_FromString(obj);

#else

        float_value = PyFloat_FromString(obj, 0);

#endif

    } else {

        PyObject* args = PyTuple_New(1);

        if (unlikely(!args)) goto bad;

        PyTuple_SET_ITEM(args, 0, obj);

        float_value = PyObject_Call((PyObject*)&PyFloat_Type, args, 0);

        PyTuple_SET_ITEM(args, 0, 0);

        Py_DECREF(args);

    }

#endif

    if (likely(float_value)) {

        double value = PyFloat_AS_DOUBLE(float_value);

        Py_DECREF(float_value);

        return value;

    }

bad:

    return (double)-1;

}


/* RaiseTooManyValuesToUnpack */

    static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {

    PyErr_Format(PyExc_ValueError,

                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);

}


/* RaiseNeedMoreValuesToUnpack */

    static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {

    PyErr_Format(PyExc_ValueError,

                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",

                 index, (index == 1) ? "" : "s");

}


/* RaiseNoneIterError */

    static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {

    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");

}


/* RaiseException */

    #if PY_MAJOR_VERSION < 3

static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,

                        CYTHON_UNUSED PyObject *cause) {

    __Pyx_PyThreadState_declare

    Py_XINCREF(type);

    if (!value || value == Py_None)

        value = NULL;

    else

        Py_INCREF(value);

    if (!tb || tb == Py_None)

        tb = NULL;

    else {

        Py_INCREF(tb);

        if (!PyTraceBack_Check(tb)) {

            PyErr_SetString(PyExc_TypeError,

                "raise: arg 3 must be a traceback or None");

            goto raise_error;

        }

    }

    if (PyType_Check(type)) {

#if CYTHON_COMPILING_IN_PYPY

        if (!value) {

            Py_INCREF(Py_None);

            value = Py_None;

        }

#endif

        PyErr_NormalizeException(&type, &value, &tb);

    } else {

        if (value) {

            PyErr_SetString(PyExc_TypeError,

                "instance exception may not have a separate value");

            goto raise_error;

        }

        value = type;

        type = (PyObject*) Py_TYPE(type);

        Py_INCREF(type);

        if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {

            PyErr_SetString(PyExc_TypeError,

                "raise: exception class must be a subclass of BaseException");

            goto raise_error;

        }

    }

    __Pyx_PyThreadState_assign

    __Pyx_ErrRestore(type, value, tb);

    return;

raise_error:

    Py_XDECREF(value);

    Py_XDECREF(type);

    Py_XDECREF(tb);

    return;

}

#else

static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {

    PyObject* owned_instance = NULL;

    if (tb == Py_None) {

        tb = 0;

    } else if (tb && !PyTraceBack_Check(tb)) {

        PyErr_SetString(PyExc_TypeError,

            "raise: arg 3 must be a traceback or None");

        goto bad;

    }

    if (value == Py_None)

        value = 0;

    if (PyExceptionInstance_Check(type)) {

        if (value) {

            PyErr_SetString(PyExc_TypeError,

                "instance exception may not have a separate value");

            goto bad;

        }

        value = type;

        type = (PyObject*) Py_TYPE(value);

    } else if (PyExceptionClass_Check(type)) {

        PyObject *instance_class = NULL;

        if (value && PyExceptionInstance_Check(value)) {

            instance_class = (PyObject*) Py_TYPE(value);

            if (instance_class != type) {

                int is_subclass = PyObject_IsSubclass(instance_class, type);

                if (!is_subclass) {

                    instance_class = NULL;

                } else if (unlikely(is_subclass == -1)) {

                    goto bad;

                } else {

                    type = instance_class;

                }

            }

        }

        if (!instance_class) {

            PyObject *args;

            if (!value)

                args = PyTuple_New(0);

            else if (PyTuple_Check(value)) {

                Py_INCREF(value);

                args = value;

            } else

                args = PyTuple_Pack(1, value);

            if (!args)

                goto bad;

            owned_instance = PyObject_Call(type, args, NULL);

            Py_DECREF(args);

            if (!owned_instance)

                goto bad;

            value = owned_instance;

            if (!PyExceptionInstance_Check(value)) {

                PyErr_Format(PyExc_TypeError,

                             "calling %R should have returned an instance of "

                             "BaseException, not %R",

                             type, Py_TYPE(value));

                goto bad;

            }

        }

    } else {

        PyErr_SetString(PyExc_TypeError,

            "raise: exception class must be a subclass of BaseException");

        goto bad;

    }

    if (cause) {

        PyObject *fixed_cause;

        if (cause == Py_None) {

            fixed_cause = NULL;

        } else if (PyExceptionClass_Check(cause)) {

            fixed_cause = PyObject_CallObject(cause, NULL);

            if (fixed_cause == NULL)

                goto bad;

        } else if (PyExceptionInstance_Check(cause)) {

            fixed_cause = cause;

            Py_INCREF(fixed_cause);

        } else {

            PyErr_SetString(PyExc_TypeError,

                            "exception causes must derive from "

                            "BaseException");

            goto bad;

        }

        PyException_SetCause(value, fixed_cause);

    }

    PyErr_SetObject(type, value);

    if (tb) {

#if CYTHON_COMPILING_IN_PYPY

        PyObject *tmp_type, *tmp_value, *tmp_tb;

        PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);

        Py_INCREF(tb);

        PyErr_Restore(tmp_type, tmp_value, tb);

        Py_XDECREF(tmp_tb);

#else

        PyThreadState *tstate = __Pyx_PyThreadState_Current;

        PyObject* tmp_tb = tstate->curexc_traceback;

        if (tb != tmp_tb) {

            Py_INCREF(tb);

            tstate->curexc_traceback = tb;

            Py_XDECREF(tmp_tb);

        }

#endif

    }

bad:

    Py_XDECREF(owned_instance);

    return;

}

#endif


/* GetTopmostException */

    #if CYTHON_USE_EXC_INFO_STACK

static _PyErr_StackItem *

__Pyx_PyErr_GetTopmostException(PyThreadState *tstate)

{

    _PyErr_StackItem *exc_info = tstate->exc_info;

    while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) &&

           exc_info->previous_item != NULL)

    {

        exc_info = exc_info->previous_item;

    }

    return exc_info;

}

#endif


/* SaveResetException */

    #if CYTHON_FAST_THREAD_STATE

static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {

    #if CYTHON_USE_EXC_INFO_STACK

    _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);

    *type = exc_info->exc_type;

    *value = exc_info->exc_value;

    *tb = exc_info->exc_traceback;

    #else

    *type = tstate->exc_type;

    *value = tstate->exc_value;

    *tb = tstate->exc_traceback;

    #endif

    Py_XINCREF(*type);

    Py_XINCREF(*value);

    Py_XINCREF(*tb);

}

static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {

    PyObject *tmp_type, *tmp_value, *tmp_tb;

    #if CYTHON_USE_EXC_INFO_STACK

    _PyErr_StackItem *exc_info = tstate->exc_info;

    tmp_type = exc_info->exc_type;

    tmp_value = exc_info->exc_value;

    tmp_tb = exc_info->exc_traceback;

    exc_info->exc_type = type;

    exc_info->exc_value = value;

    exc_info->exc_traceback = tb;

    #else

    tmp_type = tstate->exc_type;

    tmp_value = tstate->exc_value;

    tmp_tb = tstate->exc_traceback;

    tstate->exc_type = type;

    tstate->exc_value = value;

    tstate->exc_traceback = tb;

    #endif

    Py_XDECREF(tmp_type);

    Py_XDECREF(tmp_value);

    Py_XDECREF(tmp_tb);

}

#endif


/* PyErrExceptionMatches */

    #if CYTHON_FAST_THREAD_STATE

static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {

    Py_ssize_t i, n;

    n = PyTuple_GET_SIZE(tuple);

#if PY_MAJOR_VERSION >= 3

    for (i=0; i<n; i++) {

        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;

    }

#endif

    for (i=0; i<n; i++) {

        if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;

    }

    return 0;

}

static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {

    PyObject *exc_type = tstate->curexc_type;

    if (exc_type == err) return 1;

    if (unlikely(!exc_type)) return 0;

    if (unlikely(PyTuple_Check(err)))

        return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);

    return __Pyx_PyErr_GivenExceptionMatches(exc_type, err);

}

#endif


/* GetException */

    #if CYTHON_FAST_THREAD_STATE

static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb)

#else

static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb)

#endif

{

    PyObject *local_type, *local_value, *local_tb;

#if CYTHON_FAST_THREAD_STATE

    PyObject *tmp_type, *tmp_value, *tmp_tb;

    local_type = tstate->curexc_type;

    local_value = tstate->curexc_value;

    local_tb = tstate->curexc_traceback;

    tstate->curexc_type = 0;

    tstate->curexc_value = 0;

    tstate->curexc_traceback = 0;

#else

    PyErr_Fetch(&local_type, &local_value, &local_tb);

#endif

    PyErr_NormalizeException(&local_type, &local_value, &local_tb);

#if CYTHON_FAST_THREAD_STATE

    if (unlikely(tstate->curexc_type))

#else

    if (unlikely(PyErr_Occurred()))

#endif

        goto bad;

    #if PY_MAJOR_VERSION >= 3

    if (local_tb) {

        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))

            goto bad;

    }

    #endif

    Py_XINCREF(local_tb);

    Py_XINCREF(local_type);

    Py_XINCREF(local_value);

    *type = local_type;

    *value = local_value;

    *tb = local_tb;

#if CYTHON_FAST_THREAD_STATE

    #if CYTHON_USE_EXC_INFO_STACK

    {

        _PyErr_StackItem *exc_info = tstate->exc_info;

        tmp_type = exc_info->exc_type;

        tmp_value = exc_info->exc_value;

        tmp_tb = exc_info->exc_traceback;

        exc_info->exc_type = local_type;

        exc_info->exc_value = local_value;

        exc_info->exc_traceback = local_tb;

    }

    #else

    tmp_type = tstate->exc_type;

    tmp_value = tstate->exc_value;

    tmp_tb = tstate->exc_traceback;

    tstate->exc_type = local_type;

    tstate->exc_value = local_value;

    tstate->exc_traceback = local_tb;

    #endif

    Py_XDECREF(tmp_type);

    Py_XDECREF(tmp_value);

    Py_XDECREF(tmp_tb);

#else

    PyErr_SetExcInfo(local_type, local_value, local_tb);

#endif

    return 0;

bad:

    *type = 0;

    *value = 0;

    *tb = 0;

    Py_XDECREF(local_type);

    Py_XDECREF(local_value);

    Py_XDECREF(local_tb);

    return -1;

}


/* TypeImport */

    #ifndef __PYX_HAVE_RT_ImportType

#define __PYX_HAVE_RT_ImportType

static PyTypeObject *__Pyx_ImportType(PyObject *module, const char *module_name, const char *class_name,

    size_t size, enum __Pyx_ImportType_CheckSize check_size)

{

    PyObject *result = 0;

    char warning[200];

    Py_ssize_t basicsize;

#ifdef Py_LIMITED_API

    PyObject *py_basicsize;

#endif

    result = PyObject_GetAttrString(module, class_name);

    if (!result)

        goto bad;

    if (!PyType_Check(result)) {

        PyErr_Format(PyExc_TypeError,

            "%.200s.%.200s is not a type object",

            module_name, class_name);

        goto bad;

    }

#ifndef Py_LIMITED_API

    basicsize = ((PyTypeObject *)result)->tp_basicsize;

#else

    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");

    if (!py_basicsize)

        goto bad;

    basicsize = PyLong_AsSsize_t(py_basicsize);

    Py_DECREF(py_basicsize);

    py_basicsize = 0;

    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())

        goto bad;

#endif

    if ((size_t)basicsize < size) {

        PyErr_Format(PyExc_ValueError,

            "%.200s.%.200s size changed, may indicate binary incompatibility. "

            "Expected %zd from C header, got %zd from PyObject",

            module_name, class_name, size, basicsize);

        goto bad;

    }

    if (check_size == __Pyx_ImportType_CheckSize_Error && (size_t)basicsize != size) {

        PyErr_Format(PyExc_ValueError,

            "%.200s.%.200s size changed, may indicate binary incompatibility. "

            "Expected %zd from C header, got %zd from PyObject",

            module_name, class_name, size, basicsize);

        goto bad;

    }

    else if (check_size == __Pyx_ImportType_CheckSize_Warn && (size_t)basicsize > size) {

        PyOS_snprintf(warning, sizeof(warning),

            "%s.%s size changed, may indicate binary incompatibility. "

            "Expected %zd from C header, got %zd from PyObject",

            module_name, class_name, size, basicsize);

        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;

    }

    return (PyTypeObject *)result;

bad:

    Py_XDECREF(result);

    return NULL;

}

#endif


/* Import */

    static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {

    PyObject *empty_list = 0;

    PyObject *module = 0;

    PyObject *global_dict = 0;

    PyObject *empty_dict = 0;

    PyObject *list;

    #if PY_MAJOR_VERSION < 3

    PyObject *py_import;

    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);

    if (!py_import)

        goto bad;

    #endif

    if (from_list)

        list = from_list;

    else {

        empty_list = PyList_New(0);

        if (!empty_list)

            goto bad;

        list = empty_list;

    }

    global_dict = PyModule_GetDict(__pyx_m);

    if (!global_dict)

        goto bad;

    empty_dict = PyDict_New();

    if (!empty_dict)

        goto bad;

    {

        #if PY_MAJOR_VERSION >= 3

        if (level == -1) {

            if ((1) && (strchr(__Pyx_MODULE_NAME, '.'))) {

                module = PyImport_ImportModuleLevelObject(

                    name, global_dict, empty_dict, list, 1);

                if (!module) {

                    if (!PyErr_ExceptionMatches(PyExc_ImportError))

                        goto bad;

                    PyErr_Clear();

                }

            }

            level = 0;

        }

        #endif

        if (!module) {

            #if PY_MAJOR_VERSION < 3

            PyObject *py_level = PyInt_FromLong(level);

            if (!py_level)

                goto bad;

            module = PyObject_CallFunctionObjArgs(py_import,

                name, global_dict, empty_dict, list, py_level, (PyObject *)NULL);

            Py_DECREF(py_level);

            #else

            module = PyImport_ImportModuleLevelObject(

                name, global_dict, empty_dict, list, level);

            #endif

        }

    }

bad:

    #if PY_MAJOR_VERSION < 3

    Py_XDECREF(py_import);

    #endif

    Py_XDECREF(empty_list);

    Py_XDECREF(empty_dict);

    return module;

}


/* CLineInTraceback */

    #ifndef CYTHON_CLINE_IN_TRACEBACK

static int __Pyx_CLineForTraceback(CYTHON_NCP_UNUSED PyThreadState *tstate, int c_line) {

    PyObject *use_cline;

    PyObject *ptype, *pvalue, *ptraceback;

#if CYTHON_COMPILING_IN_CPYTHON

    PyObject **cython_runtime_dict;

#endif

    if (unlikely(!__pyx_cython_runtime)) {

        return c_line;

    }

    __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);

#if CYTHON_COMPILING_IN_CPYTHON

    cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);

    if (likely(cython_runtime_dict)) {

        __PYX_PY_DICT_LOOKUP_IF_MODIFIED(

            use_cline, *cython_runtime_dict,

            __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback))

    } else

#endif

    {

      PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);

      if (use_cline_obj) {

        use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;

        Py_DECREF(use_cline_obj);

      } else {

        PyErr_Clear();

        use_cline = NULL;

      }

    }

    if (!use_cline) {

        c_line = 0;

        PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);

    }

    else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) {

        c_line = 0;

    }

    __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);

    return c_line;

}

#endif


/* CodeObjectCache */

    static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {

    int start = 0, mid = 0, end = count - 1;

    if (end >= 0 && code_line > entries[end].code_line) {

        return count;

    }

    while (start < end) {

        mid = start + (end - start) / 2;

        if (code_line < entries[mid].code_line) {

            end = mid;

        } else if (code_line > entries[mid].code_line) {

             start = mid + 1;

        } else {

            return mid;

        }

    }

    if (code_line <= entries[mid].code_line) {

        return mid;

    } else {

        return mid + 1;

    }

}

static PyCodeObject *__pyx_find_code_object(int code_line) {

    PyCodeObject* code_object;

    int pos;

    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {

        return NULL;

    }

    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);

    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {

        return NULL;

    }

    code_object = __pyx_code_cache.entries[pos].code_object;

    Py_INCREF(code_object);

    return code_object;

}

static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {

    int pos, i;

    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;

    if (unlikely(!code_line)) {

        return;

    }

    if (unlikely(!entries)) {

        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));

        if (likely(entries)) {

            __pyx_code_cache.entries = entries;

            __pyx_code_cache.max_count = 64;

            __pyx_code_cache.count = 1;

            entries[0].code_line = code_line;

            entries[0].code_object = code_object;

            Py_INCREF(code_object);

        }

        return;

    }

    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);

    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {

        PyCodeObject* tmp = entries[pos].code_object;

        entries[pos].code_object = code_object;

        Py_DECREF(tmp);

        return;

    }

    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {

        int new_max = __pyx_code_cache.max_count + 64;

        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(

            __pyx_code_cache.entries, ((size_t)new_max) * sizeof(__Pyx_CodeObjectCacheEntry));

        if (unlikely(!entries)) {

            return;

        }

        __pyx_code_cache.entries = entries;

        __pyx_code_cache.max_count = new_max;

    }

    for (i=__pyx_code_cache.count; i>pos; i--) {

        entries[i] = entries[i-1];

    }

    entries[pos].code_line = code_line;

    entries[pos].code_object = code_object;

    __pyx_code_cache.count++;

    Py_INCREF(code_object);

}


/* AddTraceback */

    #include "compile.h"

#include "frameobject.h"

#include "traceback.h"

static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(

            const char *funcname, int c_line,

            int py_line, const char *filename) {

    PyCodeObject *py_code = 0;

    PyObject *py_srcfile = 0;

    PyObject *py_funcname = 0;

    #if PY_MAJOR_VERSION < 3

    py_srcfile = PyString_FromString(filename);

    #else

    py_srcfile = PyUnicode_FromString(filename);

    #endif

    if (!py_srcfile) goto bad;

    if (c_line) {

        #if PY_MAJOR_VERSION < 3

        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);

        #else

        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);

        #endif

    }

    else {

        #if PY_MAJOR_VERSION < 3

        py_funcname = PyString_FromString(funcname);

        #else

        py_funcname = PyUnicode_FromString(funcname);

        #endif

    }

    if (!py_funcname) goto bad;

    py_code = __Pyx_PyCode_New(

        0,

        0,

        0,

        0,

        0,

        __pyx_empty_bytes, /*PyObject *code,*/

        __pyx_empty_tuple, /*PyObject *consts,*/

        __pyx_empty_tuple, /*PyObject *names,*/

        __pyx_empty_tuple, /*PyObject *varnames,*/

        __pyx_empty_tuple, /*PyObject *freevars,*/

        __pyx_empty_tuple, /*PyObject *cellvars,*/

        py_srcfile,   /*PyObject *filename,*/

        py_funcname,  /*PyObject *name,*/

        py_line,

        __pyx_empty_bytes  /*PyObject *lnotab*/

    );

    Py_DECREF(py_srcfile);

    Py_DECREF(py_funcname);

    return py_code;

bad:

    Py_XDECREF(py_srcfile);

    Py_XDECREF(py_funcname);

    return NULL;

}

static void __Pyx_AddTraceback(const char *funcname, int c_line,

                               int py_line, const char *filename) {

    PyCodeObject *py_code = 0;

    PyFrameObject *py_frame = 0;

    PyThreadState *tstate = __Pyx_PyThreadState_Current;

    if (c_line) {

        c_line = __Pyx_CLineForTraceback(tstate, c_line);

    }

    py_code = __pyx_find_code_object(c_line ? -c_line : py_line);

    if (!py_code) {

        py_code = __Pyx_CreateCodeObjectForTraceback(

            funcname, c_line, py_line, filename);

        if (!py_code) goto bad;

        __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);

    }

    py_frame = PyFrame_New(

        tstate,            /*PyThreadState *tstate,*/

        py_code,           /*PyCodeObject *code,*/

        __pyx_d,    /*PyObject *globals,*/

        0                  /*PyObject *locals*/

    );

    if (!py_frame) goto bad;

    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);

    PyTraceBack_Here(py_frame);

bad:

    Py_XDECREF(py_code);

    Py_XDECREF(py_frame);

}


#if PY_MAJOR_VERSION < 3

static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {

    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);

    PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name);

    return -1;

}

static void __Pyx_ReleaseBuffer(Py_buffer *view) {

    PyObject *obj = view->obj;

    if (!obj) return;

    if (PyObject_CheckBuffer(obj)) {

        PyBuffer_Release(view);

        return;

    }

    if ((0)) {}

    view->obj = NULL;

    Py_DECREF(obj);

}

#endif


    /* CIntFromPyVerify */

    #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\

    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)

#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\

    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)

#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\

    {\

        func_type value = func_value;\

        if (sizeof(target_type) < sizeof(func_type)) {\

            if (unlikely(value != (func_type) (target_type) value)) {\

                func_type zero = 0;\

                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\

                    return (target_type) -1;\

                if (is_unsigned && unlikely(value < zero))\

                    goto raise_neg_overflow;\

                else\

                    goto raise_overflow;\

            }\

        }\

        return (target_type) value;\

    }


/* CIntToPy */

    static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {

    const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;

    const int is_unsigned = neg_one > const_zero;

    if (is_unsigned) {

        if (sizeof(int) < sizeof(long)) {

            return PyInt_FromLong((long) value);

        } else if (sizeof(int) <= sizeof(unsigned long)) {

            return PyLong_FromUnsignedLong((unsigned long) value);

#ifdef HAVE_LONG_LONG

        } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {

            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);

#endif

        }

    } else {

        if (sizeof(int) <= sizeof(long)) {

            return PyInt_FromLong((long) value);

#ifdef HAVE_LONG_LONG

        } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {

            return PyLong_FromLongLong((PY_LONG_LONG) value);

#endif

        }

    }

    {

        int one = 1; int little = (int)*(unsigned char *)&one;

        unsigned char *bytes = (unsigned char *)&value;

        return _PyLong_FromByteArray(bytes, sizeof(int),

                                     little, !is_unsigned);

    }

}


/* CIntToPy */

    static CYTHON_INLINE PyObject* __Pyx_PyInt_From_Py_intptr_t(Py_intptr_t value) {

    const Py_intptr_t neg_one = (Py_intptr_t) ((Py_intptr_t) 0 - (Py_intptr_t) 1), const_zero = (Py_intptr_t) 0;

    const int is_unsigned = neg_one > const_zero;

    if (is_unsigned) {

        if (sizeof(Py_intptr_t) < sizeof(long)) {

            return PyInt_FromLong((long) value);

        } else if (sizeof(Py_intptr_t) <= sizeof(unsigned long)) {

            return PyLong_FromUnsignedLong((unsigned long) value);

#ifdef HAVE_LONG_LONG

        } else if (sizeof(Py_intptr_t) <= sizeof(unsigned PY_LONG_LONG)) {

            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);

#endif

        }

    } else {

        if (sizeof(Py_intptr_t) <= sizeof(long)) {

            return PyInt_FromLong((long) value);

#ifdef HAVE_LONG_LONG

        } else if (sizeof(Py_intptr_t) <= sizeof(PY_LONG_LONG)) {

            return PyLong_FromLongLong((PY_LONG_LONG) value);

#endif

        }

    }

    {

        int one = 1; int little = (int)*(unsigned char *)&one;

        unsigned char *bytes = (unsigned char *)&value;

        return _PyLong_FromByteArray(bytes, sizeof(Py_intptr_t),

                                     little, !is_unsigned);

    }

}


/* CIntToPy */

    static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {

    const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0;

    const int is_unsigned = neg_one > const_zero;

    if (is_unsigned) {

        if (sizeof(long) < sizeof(long)) {

            return PyInt_FromLong((long) value);

        } else if (sizeof(long) <= sizeof(unsigned long)) {

            return PyLong_FromUnsignedLong((unsigned long) value);

#ifdef HAVE_LONG_LONG

        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {

            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);

#endif

        }

    } else {

        if (sizeof(long) <= sizeof(long)) {

            return PyInt_FromLong((long) value);

#ifdef HAVE_LONG_LONG

        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {

            return PyLong_FromLongLong((PY_LONG_LONG) value);

#endif

        }

    }

    {

        int one = 1; int little = (int)*(unsigned char *)&one;

        unsigned char *bytes = (unsigned char *)&value;

        return _PyLong_FromByteArray(bytes, sizeof(long),

                                     little, !is_unsigned);

    }

}


/* Declarations */

    #if CYTHON_CCOMPLEX

  #ifdef __cplusplus

    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {

      return ::std::complex< float >(x, y);

    }

  #else

    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {

      return x + y*(__pyx_t_float_complex)_Complex_I;

    }

  #endif

#else

    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {

      __pyx_t_float_complex z;

      z.real = x;

      z.imag = y;

      return z;

    }

#endif


/* Arithmetic */

    #if CYTHON_CCOMPLEX

#else

    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {

       return (a.real == b.real) && (a.imag == b.imag);

    }

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {

        __pyx_t_float_complex z;

        z.real = a.real + b.real;

        z.imag = a.imag + b.imag;

        return z;

    }

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {

        __pyx_t_float_complex z;

        z.real = a.real - b.real;

        z.imag = a.imag - b.imag;

        return z;

    }

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {

        __pyx_t_float_complex z;

        z.real = a.real * b.real - a.imag * b.imag;

        z.imag = a.real * b.imag + a.imag * b.real;

        return z;

    }

    #if 1

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {

        if (b.imag == 0) {

            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);

        } else if (fabsf(b.real) >= fabsf(b.imag)) {

            if (b.real == 0 && b.imag == 0) {

                return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag);

            } else {

                float r = b.imag / b.real;

                float s = (float)(1.0) / (b.real + b.imag * r);

                return __pyx_t_float_complex_from_parts(

                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);

            }

        } else {

            float r = b.real / b.imag;

            float s = (float)(1.0) / (b.imag + b.real * r);

            return __pyx_t_float_complex_from_parts(

                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);

        }

    }

    #else

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {

        if (b.imag == 0) {

            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);

        } else {

            float denom = b.real * b.real + b.imag * b.imag;

            return __pyx_t_float_complex_from_parts(

                (a.real * b.real + a.imag * b.imag) / denom,

                (a.imag * b.real - a.real * b.imag) / denom);

        }

    }

    #endif

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) {

        __pyx_t_float_complex z;

        z.real = -a.real;

        z.imag = -a.imag;

        return z;

    }

    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) {

       return (a.real == 0) && (a.imag == 0);

    }

    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) {

        __pyx_t_float_complex z;

        z.real =  a.real;

        z.imag = -a.imag;

        return z;

    }

    #if 1

        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) {

          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)

            return sqrtf(z.real*z.real + z.imag*z.imag);

          #else

            return hypotf(z.real, z.imag);

          #endif

        }

        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {

            __pyx_t_float_complex z;

            float r, lnr, theta, z_r, z_theta;

            if (b.imag == 0 && b.real == (int)b.real) {

                if (b.real < 0) {

                    float denom = a.real * a.real + a.imag * a.imag;

                    a.real = a.real / denom;

                    a.imag = -a.imag / denom;

                    b.real = -b.real;

                }

                switch ((int)b.real) {

                    case 0:

                        z.real = 1;

                        z.imag = 0;

                        return z;

                    case 1:

                        return a;

                    case 2:

                        return __Pyx_c_prod_float(a, a);

                    case 3:

                        z = __Pyx_c_prod_float(a, a);

                        return __Pyx_c_prod_float(z, a);

                    case 4:

                        z = __Pyx_c_prod_float(a, a);

                        return __Pyx_c_prod_float(z, z);

                }

            }

            if (a.imag == 0) {

                if (a.real == 0) {

                    return a;

                } else if (b.imag == 0) {

                    z.real = powf(a.real, b.real);

                    z.imag = 0;

                    return z;

                } else if (a.real > 0) {

                    r = a.real;

                    theta = 0;

                } else {

                    r = -a.real;

                    theta = atan2f(0.0, -1.0);

                }

            } else {

                r = __Pyx_c_abs_float(a);

                theta = atan2f(a.imag, a.real);

            }

            lnr = logf(r);

            z_r = expf(lnr * b.real - theta * b.imag);

            z_theta = theta * b.real + lnr * b.imag;

            z.real = z_r * cosf(z_theta);

            z.imag = z_r * sinf(z_theta);

            return z;

        }

    #endif

#endif


/* Declarations */

    #if CYTHON_CCOMPLEX

  #ifdef __cplusplus

    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {

      return ::std::complex< double >(x, y);

    }

  #else

    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {

      return x + y*(__pyx_t_double_complex)_Complex_I;

    }

  #endif

#else

    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {

      __pyx_t_double_complex z;

      z.real = x;

      z.imag = y;

      return z;

    }

#endif


/* Arithmetic */

    #if CYTHON_CCOMPLEX

#else

    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {

       return (a.real == b.real) && (a.imag == b.imag);

    }

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {

        __pyx_t_double_complex z;

        z.real = a.real + b.real;

        z.imag = a.imag + b.imag;

        return z;

    }

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {

        __pyx_t_double_complex z;

        z.real = a.real - b.real;

        z.imag = a.imag - b.imag;

        return z;

    }

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {

        __pyx_t_double_complex z;

        z.real = a.real * b.real - a.imag * b.imag;

        z.imag = a.real * b.imag + a.imag * b.real;

        return z;

    }

    #if 1

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {

        if (b.imag == 0) {

            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);

        } else if (fabs(b.real) >= fabs(b.imag)) {

            if (b.real == 0 && b.imag == 0) {

                return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag);

            } else {

                double r = b.imag / b.real;

                double s = (double)(1.0) / (b.real + b.imag * r);

                return __pyx_t_double_complex_from_parts(

                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);

            }

        } else {

            double r = b.real / b.imag;

            double s = (double)(1.0) / (b.imag + b.real * r);

            return __pyx_t_double_complex_from_parts(

                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);

        }

    }

    #else

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {

        if (b.imag == 0) {

            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);

        } else {

            double denom = b.real * b.real + b.imag * b.imag;

            return __pyx_t_double_complex_from_parts(

                (a.real * b.real + a.imag * b.imag) / denom,

                (a.imag * b.real - a.real * b.imag) / denom);

        }

    }

    #endif

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) {

        __pyx_t_double_complex z;

        z.real = -a.real;

        z.imag = -a.imag;

        return z;

    }

    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) {

       return (a.real == 0) && (a.imag == 0);

    }

    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) {

        __pyx_t_double_complex z;

        z.real =  a.real;

        z.imag = -a.imag;

        return z;

    }

    #if 1

        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) {

          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)

            return sqrt(z.real*z.real + z.imag*z.imag);

          #else

            return hypot(z.real, z.imag);

          #endif

        }

        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {

            __pyx_t_double_complex z;

            double r, lnr, theta, z_r, z_theta;

            if (b.imag == 0 && b.real == (int)b.real) {

                if (b.real < 0) {

                    double denom = a.real * a.real + a.imag * a.imag;

                    a.real = a.real / denom;

                    a.imag = -a.imag / denom;

                    b.real = -b.real;

                }

                switch ((int)b.real) {

                    case 0:

                        z.real = 1;

                        z.imag = 0;

                        return z;

                    case 1:

                        return a;

                    case 2:

                        return __Pyx_c_prod_double(a, a);

                    case 3:

                        z = __Pyx_c_prod_double(a, a);

                        return __Pyx_c_prod_double(z, a);

                    case 4:

                        z = __Pyx_c_prod_double(a, a);

                        return __Pyx_c_prod_double(z, z);

                }

            }

            if (a.imag == 0) {

                if (a.real == 0) {

                    return a;

                } else if (b.imag == 0) {

                    z.real = pow(a.real, b.real);

                    z.imag = 0;

                    return z;

                } else if (a.real > 0) {

                    r = a.real;

                    theta = 0;

                } else {

                    r = -a.real;

                    theta = atan2(0.0, -1.0);

                }

            } else {

                r = __Pyx_c_abs_double(a);

                theta = atan2(a.imag, a.real);

            }

            lnr = log(r);

            z_r = exp(lnr * b.real - theta * b.imag);

            z_theta = theta * b.real + lnr * b.imag;

            z.real = z_r * cos(z_theta);

            z.imag = z_r * sin(z_theta);

            return z;

        }

    #endif

#endif


/* CIntToPy */

    static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value) {

    const enum NPY_TYPES neg_one = (enum NPY_TYPES) ((enum NPY_TYPES) 0 - (enum NPY_TYPES) 1), const_zero = (enum NPY_TYPES) 0;

    const int is_unsigned = neg_one > const_zero;

    if (is_unsigned) {

        if (sizeof(enum NPY_TYPES) < sizeof(long)) {

            return PyInt_FromLong((long) value);

        } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned long)) {

            return PyLong_FromUnsignedLong((unsigned long) value);

#ifdef HAVE_LONG_LONG

        } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned PY_LONG_LONG)) {

            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);

#endif

        }

    } else {

        if (sizeof(enum NPY_TYPES) <= sizeof(long)) {

            return PyInt_FromLong((long) value);

#ifdef HAVE_LONG_LONG

        } else if (sizeof(enum NPY_TYPES) <= sizeof(PY_LONG_LONG)) {

            return PyLong_FromLongLong((PY_LONG_LONG) value);

#endif

        }

    }

    {

        int one = 1; int little = (int)*(unsigned char *)&one;

        unsigned char *bytes = (unsigned char *)&value;

        return _PyLong_FromByteArray(bytes, sizeof(enum NPY_TYPES),

                                     little, !is_unsigned);

    }

}


/* CIntFromPy */

    static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {

    const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;

    const int is_unsigned = neg_one > const_zero;

#if PY_MAJOR_VERSION < 3

    if (likely(PyInt_Check(x))) {

        if (sizeof(int) < sizeof(long)) {

            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))

        } else {

            long val = PyInt_AS_LONG(x);

            if (is_unsigned && unlikely(val < 0)) {

                goto raise_neg_overflow;

            }

            return (int) val;

        }

    } else

#endif

    if (likely(PyLong_Check(x))) {

        if (is_unsigned) {

#if CYTHON_USE_PYLONG_INTERNALS

            const digit* digits = ((PyLongObject*)x)->ob_digit;

            switch (Py_SIZE(x)) {

                case  0: return (int) 0;

                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])

                case 2:

                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {

                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));

                        }

                    }

                    break;

                case 3:

                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {

                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));

                        }

                    }

                    break;

                case 4:

                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {

                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));

                        }

                    }

                    break;

            }

#endif

#if CYTHON_COMPILING_IN_CPYTHON

            if (unlikely(Py_SIZE(x) < 0)) {

                goto raise_neg_overflow;

            }

#else

            {

                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);

                if (unlikely(result < 0))

                    return (int) -1;

                if (unlikely(result == 1))

                    goto raise_neg_overflow;

            }

#endif

            if (sizeof(int) <= sizeof(unsigned long)) {

                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))

#ifdef HAVE_LONG_LONG

            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {

                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))

#endif

            }

        } else {

#if CYTHON_USE_PYLONG_INTERNALS

            const digit* digits = ((PyLongObject*)x)->ob_digit;

            switch (Py_SIZE(x)) {

                case  0: return (int) 0;

                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))

                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])

                case -2:

                    if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {

                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));

                        }

                    }

                    break;

                case 2:

                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {

                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));

                        }

                    }

                    break;

                case -3:

                    if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {

                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));

                        }

                    }

                    break;

                case 3:

                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {

                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));

                        }

                    }

                    break;

                case -4:

                    if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {

                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));

                        }

                    }

                    break;

                case 4:

                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {

                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));

                        }

                    }

                    break;

            }

#endif

            if (sizeof(int) <= sizeof(long)) {

                __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))

#ifdef HAVE_LONG_LONG

            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {

                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))

#endif

            }

        }

        {

#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)

            PyErr_SetString(PyExc_RuntimeError,

                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");

#else

            int val;

            PyObject *v = __Pyx_PyNumber_IntOrLong(x);

 #if PY_MAJOR_VERSION < 3

            if (likely(v) && !PyLong_Check(v)) {

                PyObject *tmp = v;

                v = PyNumber_Long(tmp);

                Py_DECREF(tmp);

            }

 #endif

            if (likely(v)) {

                int one = 1; int is_little = (int)*(unsigned char *)&one;

                unsigned char *bytes = (unsigned char *)&val;

                int ret = _PyLong_AsByteArray((PyLongObject *)v,

                                              bytes, sizeof(val),

                                              is_little, !is_unsigned);

                Py_DECREF(v);

                if (likely(!ret))

                    return val;

            }

#endif

            return (int) -1;

        }

    } else {

        int val;

        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);

        if (!tmp) return (int) -1;

        val = __Pyx_PyInt_As_int(tmp);

        Py_DECREF(tmp);

        return val;

    }

raise_overflow:

    PyErr_SetString(PyExc_OverflowError,

        "value too large to convert to int");

    return (int) -1;

raise_neg_overflow:

    PyErr_SetString(PyExc_OverflowError,

        "can't convert negative value to int");

    return (int) -1;

}


/* CIntFromPy */

    static CYTHON_INLINE Py_intptr_t __Pyx_PyInt_As_Py_intptr_t(PyObject *x) {

    const Py_intptr_t neg_one = (Py_intptr_t) ((Py_intptr_t) 0 - (Py_intptr_t) 1), const_zero = (Py_intptr_t) 0;

    const int is_unsigned = neg_one > const_zero;

#if PY_MAJOR_VERSION < 3

    if (likely(PyInt_Check(x))) {

        if (sizeof(Py_intptr_t) < sizeof(long)) {

            __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, PyInt_AS_LONG(x))

        } else {

            long val = PyInt_AS_LONG(x);

            if (is_unsigned && unlikely(val < 0)) {

                goto raise_neg_overflow;

            }

            return (Py_intptr_t) val;

        }

    } else

#endif

    if (likely(PyLong_Check(x))) {

        if (is_unsigned) {

#if CYTHON_USE_PYLONG_INTERNALS

            const digit* digits = ((PyLongObject*)x)->ob_digit;

            switch (Py_SIZE(x)) {

                case  0: return (Py_intptr_t) 0;

                case  1: __PYX_VERIFY_RETURN_INT(Py_intptr_t, digit, digits[0])

                case 2:

                    if (8 * sizeof(Py_intptr_t) > 1 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(Py_intptr_t) >= 2 * PyLong_SHIFT) {

                            return (Py_intptr_t) (((((Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0]));

                        }

                    }

                    break;

                case 3:

                    if (8 * sizeof(Py_intptr_t) > 2 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(Py_intptr_t) >= 3 * PyLong_SHIFT) {

                            return (Py_intptr_t) (((((((Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0]));

                        }

                    }

                    break;

                case 4:

                    if (8 * sizeof(Py_intptr_t) > 3 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(Py_intptr_t) >= 4 * PyLong_SHIFT) {

                            return (Py_intptr_t) (((((((((Py_intptr_t)digits[3]) << PyLong_SHIFT) | (Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0]));

                        }

                    }

                    break;

            }

#endif

#if CYTHON_COMPILING_IN_CPYTHON

            if (unlikely(Py_SIZE(x) < 0)) {

                goto raise_neg_overflow;

            }

#else

            {

                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);

                if (unlikely(result < 0))

                    return (Py_intptr_t) -1;

                if (unlikely(result == 1))

                    goto raise_neg_overflow;

            }

#endif

            if (sizeof(Py_intptr_t) <= sizeof(unsigned long)) {

                __PYX_VERIFY_RETURN_INT_EXC(Py_intptr_t, unsigned long, PyLong_AsUnsignedLong(x))

#ifdef HAVE_LONG_LONG

            } else if (sizeof(Py_intptr_t) <= sizeof(unsigned PY_LONG_LONG)) {

                __PYX_VERIFY_RETURN_INT_EXC(Py_intptr_t, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))

#endif

            }

        } else {

#if CYTHON_USE_PYLONG_INTERNALS

            const digit* digits = ((PyLongObject*)x)->ob_digit;

            switch (Py_SIZE(x)) {

                case  0: return (Py_intptr_t) 0;

                case -1: __PYX_VERIFY_RETURN_INT(Py_intptr_t, sdigit, (sdigit) (-(sdigit)digits[0]))

                case  1: __PYX_VERIFY_RETURN_INT(Py_intptr_t,  digit, +digits[0])

                case -2:

                    if (8 * sizeof(Py_intptr_t) - 1 > 1 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(Py_intptr_t) - 1 > 2 * PyLong_SHIFT) {

                            return (Py_intptr_t) (((Py_intptr_t)-1)*(((((Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));

                        }

                    }

                    break;

                case 2:

                    if (8 * sizeof(Py_intptr_t) > 1 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(Py_intptr_t) - 1 > 2 * PyLong_SHIFT) {

                            return (Py_intptr_t) ((((((Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));

                        }

                    }

                    break;

                case -3:

                    if (8 * sizeof(Py_intptr_t) - 1 > 2 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(Py_intptr_t) - 1 > 3 * PyLong_SHIFT) {

                            return (Py_intptr_t) (((Py_intptr_t)-1)*(((((((Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));

                        }

                    }

                    break;

                case 3:

                    if (8 * sizeof(Py_intptr_t) > 2 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(Py_intptr_t) - 1 > 3 * PyLong_SHIFT) {

                            return (Py_intptr_t) ((((((((Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));

                        }

                    }

                    break;

                case -4:

                    if (8 * sizeof(Py_intptr_t) - 1 > 3 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(Py_intptr_t) - 1 > 4 * PyLong_SHIFT) {

                            return (Py_intptr_t) (((Py_intptr_t)-1)*(((((((((Py_intptr_t)digits[3]) << PyLong_SHIFT) | (Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));

                        }

                    }

                    break;

                case 4:

                    if (8 * sizeof(Py_intptr_t) > 3 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(Py_intptr_t) - 1 > 4 * PyLong_SHIFT) {

                            return (Py_intptr_t) ((((((((((Py_intptr_t)digits[3]) << PyLong_SHIFT) | (Py_intptr_t)digits[2]) << PyLong_SHIFT) | (Py_intptr_t)digits[1]) << PyLong_SHIFT) | (Py_intptr_t)digits[0])));

                        }

                    }

                    break;

            }

#endif

            if (sizeof(Py_intptr_t) <= sizeof(long)) {

                __PYX_VERIFY_RETURN_INT_EXC(Py_intptr_t, long, PyLong_AsLong(x))

#ifdef HAVE_LONG_LONG

            } else if (sizeof(Py_intptr_t) <= sizeof(PY_LONG_LONG)) {

                __PYX_VERIFY_RETURN_INT_EXC(Py_intptr_t, PY_LONG_LONG, PyLong_AsLongLong(x))

#endif

            }

        }

        {

#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)

            PyErr_SetString(PyExc_RuntimeError,

                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");

#else

            Py_intptr_t val;

            PyObject *v = __Pyx_PyNumber_IntOrLong(x);

 #if PY_MAJOR_VERSION < 3

            if (likely(v) && !PyLong_Check(v)) {

                PyObject *tmp = v;

                v = PyNumber_Long(tmp);

                Py_DECREF(tmp);

            }

 #endif

            if (likely(v)) {

                int one = 1; int is_little = (int)*(unsigned char *)&one;

                unsigned char *bytes = (unsigned char *)&val;

                int ret = _PyLong_AsByteArray((PyLongObject *)v,

                                              bytes, sizeof(val),

                                              is_little, !is_unsigned);

                Py_DECREF(v);

                if (likely(!ret))

                    return val;

            }

#endif

            return (Py_intptr_t) -1;

        }

    } else {

        Py_intptr_t val;

        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);

        if (!tmp) return (Py_intptr_t) -1;

        val = __Pyx_PyInt_As_Py_intptr_t(tmp);

        Py_DECREF(tmp);

        return val;

    }

raise_overflow:

    PyErr_SetString(PyExc_OverflowError,

        "value too large to convert to Py_intptr_t");

    return (Py_intptr_t) -1;

raise_neg_overflow:

    PyErr_SetString(PyExc_OverflowError,

        "can't convert negative value to Py_intptr_t");

    return (Py_intptr_t) -1;

}


/* CIntFromPy */

    static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {

    const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0;

    const int is_unsigned = neg_one > const_zero;

#if PY_MAJOR_VERSION < 3

    if (likely(PyInt_Check(x))) {

        if (sizeof(long) < sizeof(long)) {

            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))

        } else {

            long val = PyInt_AS_LONG(x);

            if (is_unsigned && unlikely(val < 0)) {

                goto raise_neg_overflow;

            }

            return (long) val;

        }

    } else

#endif

    if (likely(PyLong_Check(x))) {

        if (is_unsigned) {

#if CYTHON_USE_PYLONG_INTERNALS

            const digit* digits = ((PyLongObject*)x)->ob_digit;

            switch (Py_SIZE(x)) {

                case  0: return (long) 0;

                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])

                case 2:

                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {

                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));

                        }

                    }

                    break;

                case 3:

                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {

                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));

                        }

                    }

                    break;

                case 4:

                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {

                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));

                        }

                    }

                    break;

            }

#endif

#if CYTHON_COMPILING_IN_CPYTHON

            if (unlikely(Py_SIZE(x) < 0)) {

                goto raise_neg_overflow;

            }

#else

            {

                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);

                if (unlikely(result < 0))

                    return (long) -1;

                if (unlikely(result == 1))

                    goto raise_neg_overflow;

            }

#endif

            if (sizeof(long) <= sizeof(unsigned long)) {

                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))

#ifdef HAVE_LONG_LONG

            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {

                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))

#endif

            }

        } else {

#if CYTHON_USE_PYLONG_INTERNALS

            const digit* digits = ((PyLongObject*)x)->ob_digit;

            switch (Py_SIZE(x)) {

                case  0: return (long) 0;

                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))

                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])

                case -2:

                    if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {

                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));

                        }

                    }

                    break;

                case 2:

                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {

                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));

                        }

                    }

                    break;

                case -3:

                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {

                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));

                        }

                    }

                    break;

                case 3:

                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {

                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));

                        }

                    }

                    break;

                case -4:

                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {

                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));

                        }

                    }

                    break;

                case 4:

                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {

                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {

                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))

                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {

                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));

                        }

                    }

                    break;

            }

#endif

            if (sizeof(long) <= sizeof(long)) {

                __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))

#ifdef HAVE_LONG_LONG

            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {

                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))

#endif

            }

        }

        {

#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)

            PyErr_SetString(PyExc_RuntimeError,

                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");

#else

            long val;

            PyObject *v = __Pyx_PyNumber_IntOrLong(x);

 #if PY_MAJOR_VERSION < 3

            if (likely(v) && !PyLong_Check(v)) {

                PyObject *tmp = v;

                v = PyNumber_Long(tmp);

                Py_DECREF(tmp);

            }

 #endif

            if (likely(v)) {

                int one = 1; int is_little = (int)*(unsigned char *)&one;

                unsigned char *bytes = (unsigned char *)&val;

                int ret = _PyLong_AsByteArray((PyLongObject *)v,

                                              bytes, sizeof(val),

                                              is_little, !is_unsigned);

                Py_DECREF(v);

                if (likely(!ret))

                    return val;

            }

#endif

            return (long) -1;

        }

    } else {

        long val;

        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);

        if (!tmp) return (long) -1;

        val = __Pyx_PyInt_As_long(tmp);

        Py_DECREF(tmp);

        return val;

    }

raise_overflow:

    PyErr_SetString(PyExc_OverflowError,

        "value too large to convert to long");

    return (long) -1;

raise_neg_overflow:

    PyErr_SetString(PyExc_OverflowError,

        "can't convert negative value to long");

    return (long) -1;

}


/* FastTypeChecks */

    #if CYTHON_COMPILING_IN_CPYTHON

static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {

    while (a) {

        a = a->tp_base;

        if (a == b)

            return 1;

    }

    return b == &PyBaseObject_Type;

}

static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {

    PyObject *mro;

    if (a == b) return 1;

    mro = a->tp_mro;

    if (likely(mro)) {

        Py_ssize_t i, n;

        n = PyTuple_GET_SIZE(mro);

        for (i = 0; i < n; i++) {

            if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)

                return 1;

        }

        return 0;

    }

    return __Pyx_InBases(a, b);

}

#if PY_MAJOR_VERSION == 2

static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {

    PyObject *exception, *value, *tb;

    int res;

    __Pyx_PyThreadState_declare

    __Pyx_PyThreadState_assign

    __Pyx_ErrFetch(&exception, &value, &tb);

    res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;

    if (unlikely(res == -1)) {

        PyErr_WriteUnraisable(err);

        res = 0;

    }

    if (!res) {

        res = PyObject_IsSubclass(err, exc_type2);

        if (unlikely(res == -1)) {

            PyErr_WriteUnraisable(err);

            res = 0;

        }

    }

    __Pyx_ErrRestore(exception, value, tb);

    return res;

}

#else

static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {

    int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;

    if (!res) {

        res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);

    }

    return res;

}

#endif

static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {

    Py_ssize_t i, n;

    assert(PyExceptionClass_Check(exc_type));

    n = PyTuple_GET_SIZE(tuple);

#if PY_MAJOR_VERSION >= 3

    for (i=0; i<n; i++) {

        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;

    }

#endif

    for (i=0; i<n; i++) {

        PyObject *t = PyTuple_GET_ITEM(tuple, i);

        #if PY_MAJOR_VERSION < 3

        if (likely(exc_type == t)) return 1;

        #endif

        if (likely(PyExceptionClass_Check(t))) {

            if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;

        } else {

        }

    }

    return 0;

}

static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {

    if (likely(err == exc_type)) return 1;

    if (likely(PyExceptionClass_Check(err))) {

        if (likely(PyExceptionClass_Check(exc_type))) {

            return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);

        } else if (likely(PyTuple_Check(exc_type))) {

            return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);

        } else {

        }

    }

    return PyErr_GivenExceptionMatches(err, exc_type);

}

static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {

    assert(PyExceptionClass_Check(exc_type1));

    assert(PyExceptionClass_Check(exc_type2));

    if (likely(err == exc_type1 || err == exc_type2)) return 1;

    if (likely(PyExceptionClass_Check(err))) {

        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);

    }

    return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));

}

#endif


/* CheckBinaryVersion */

    static int __Pyx_check_binary_version(void) {

    char ctversion[4], rtversion[4];

    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);

    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());

    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {

        char message[200];

        PyOS_snprintf(message, sizeof(message),

                      "compiletime version %s of module '%.100s' "

                      "does not match runtime version %s",

                      ctversion, __Pyx_MODULE_NAME, rtversion);

        return PyErr_WarnEx(NULL, message, 1);

    }

    return 0;

}


/* InitStrings */

    static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {

    while (t->p) {

        #if PY_MAJOR_VERSION < 3

        if (t->is_unicode) {

            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);

        } else if (t->intern) {

            *t->p = PyString_InternFromString(t->s);

        } else {

            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);

        }

        #else

        if (t->is_unicode | t->is_str) {

            if (t->intern) {

                *t->p = PyUnicode_InternFromString(t->s);

            } else if (t->encoding) {

                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);

            } else {

                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);

            }

        } else {

            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);

        }

        #endif

        if (!*t->p)

            return -1;

        if (PyObject_Hash(*t->p) == -1)

            return -1;

        ++t;

    }

    return 0;

}


static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {

    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));

}

static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {

    Py_ssize_t ignore;

    return __Pyx_PyObject_AsStringAndSize(o, &ignore);

}

#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT

#if !CYTHON_PEP393_ENABLED

static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {

    char* defenc_c;

    PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);

    if (!defenc) return NULL;

    defenc_c = PyBytes_AS_STRING(defenc);

#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII

    {

        char* end = defenc_c + PyBytes_GET_SIZE(defenc);

        char* c;

        for (c = defenc_c; c < end; c++) {

            if ((unsigned char) (*c) >= 128) {

                PyUnicode_AsASCIIString(o);

                return NULL;

            }

        }

    }

#endif

    *length = PyBytes_GET_SIZE(defenc);

    return defenc_c;

}

#else

static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {

    if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;

#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII

    if (likely(PyUnicode_IS_ASCII(o))) {

        *length = PyUnicode_GET_LENGTH(o);

        return PyUnicode_AsUTF8(o);

    } else {

        PyUnicode_AsASCIIString(o);

        return NULL;

    }

#else

    return PyUnicode_AsUTF8AndSize(o, length);

#endif

}

#endif

#endif

static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {

#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT

    if (

#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII

            __Pyx_sys_getdefaultencoding_not_ascii &&

#endif

            PyUnicode_Check(o)) {

        return __Pyx_PyUnicode_AsStringAndSize(o, length);

    } else

#endif

#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))

    if (PyByteArray_Check(o)) {

        *length = PyByteArray_GET_SIZE(o);

        return PyByteArray_AS_STRING(o);

    } else

#endif

    {

        char* result;

        int r = PyBytes_AsStringAndSize(o, &result, length);

        if (unlikely(r < 0)) {

            return NULL;

        } else {

            return result;

        }

    }

}

static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {

   int is_true = x == Py_True;

   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;

   else return PyObject_IsTrue(x);

}

static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {

    int retval;

    if (unlikely(!x)) return -1;

    retval = __Pyx_PyObject_IsTrue(x);

    Py_DECREF(x);

    return retval;

}

static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {

#if PY_MAJOR_VERSION >= 3

    if (PyLong_Check(result)) {

        if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,

                "__int__ returned non-int (type %.200s).  "

                "The ability to return an instance of a strict subclass of int "

                "is deprecated, and may be removed in a future version of Python.",

                Py_TYPE(result)->tp_name)) {

            Py_DECREF(result);

            return NULL;

        }

        return result;

    }

#endif

    PyErr_Format(PyExc_TypeError,

                 "__%.4s__ returned non-%.4s (type %.200s)",

                 type_name, type_name, Py_TYPE(result)->tp_name);

    Py_DECREF(result);

    return NULL;

}

static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {

#if CYTHON_USE_TYPE_SLOTS

  PyNumberMethods *m;

#endif

  const char *name = NULL;

  PyObject *res = NULL;

#if PY_MAJOR_VERSION < 3

  if (likely(PyInt_Check(x) || PyLong_Check(x)))

#else

  if (likely(PyLong_Check(x)))

#endif

    return __Pyx_NewRef(x);

#if CYTHON_USE_TYPE_SLOTS

  m = Py_TYPE(x)->tp_as_number;

  #if PY_MAJOR_VERSION < 3

  if (m && m->nb_int) {

    name = "int";

    res = m->nb_int(x);

  }

  else if (m && m->nb_long) {

    name = "long";

    res = m->nb_long(x);

  }

  #else

  if (likely(m && m->nb_int)) {

    name = "int";

    res = m->nb_int(x);

  }

  #endif

#else

  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {

    res = PyNumber_Int(x);

  }

#endif

  if (likely(res)) {

#if PY_MAJOR_VERSION < 3

    if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {

#else

    if (unlikely(!PyLong_CheckExact(res))) {

#endif

        return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);

    }

  }

  else if (!PyErr_Occurred()) {

    PyErr_SetString(PyExc_TypeError,

                    "an integer is required");

  }

  return res;

}

static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {

  Py_ssize_t ival;

  PyObject *x;

#if PY_MAJOR_VERSION < 3

  if (likely(PyInt_CheckExact(b))) {

    if (sizeof(Py_ssize_t) >= sizeof(long))

        return PyInt_AS_LONG(b);

    else

        return PyInt_AsSsize_t(b);

  }

#endif

  if (likely(PyLong_CheckExact(b))) {

    #if CYTHON_USE_PYLONG_INTERNALS

    const digit* digits = ((PyLongObject*)b)->ob_digit;

    const Py_ssize_t size = Py_SIZE(b);

    if (likely(__Pyx_sst_abs(size) <= 1)) {

        ival = likely(size) ? digits[0] : 0;

        if (size == -1) ival = -ival;

        return ival;

    } else {

      switch (size) {

         case 2:

           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {

             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));

           }

           break;

         case -2:

           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {

             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));

           }

           break;

         case 3:

           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {

             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));

           }

           break;

         case -3:

           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {

             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));

           }

           break;

         case 4:

           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {

             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));

           }

           break;

         case -4:

           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {

             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));

           }

           break;

      }

    }

    #endif

    return PyLong_AsSsize_t(b);

  }

  x = PyNumber_Index(b);

  if (!x) return -1;

  ival = PyInt_AsSsize_t(x);

  Py_DECREF(x);

  return ival;

}

static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {

  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);

}

static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {

    return PyInt_FromSize_t(ival);

}


#endif /* Py_PYTHON_H */